Operational amplifier: switching circuits, operating principle. Non-inverting operational amplifier amplifier circuit

The controller calculates the error (the difference between the reference signal and the feedback signal) and converts it into a control action in accordance with a certain mathematical operation.

The ACS mainly uses the following types of controllers: proportional (P), integral (I) and proportional-integral (PI). Depending on the type of converted signals, analogue and digital regulators are distinguished.

Analog regulators(AR) are implemented based on operational amplifiers, digital- based on specialized computing devices or microprocessors. Analog controllers only convert analog signals that are continuous functions of time. When passing through the AP, each instantaneous value of a continuous signal is converted.

To implement AR, an operational amplifier (op-amp) is connected according to a summing amplifier circuit with negative feedback. The type of regulator and its transfer function are determined by the circuit for connecting resistors and capacitors in the circuits at the input and in the op-amp feedback.

A proportional controller (P-regulator) is implemented by connecting an op-amp resistor with resistance R os to the feedback circuit. This controller is characterized by a proportionality coefficient To , which can be either greater or less than one.

An integral regulator (I-regulator) is implemented when an op-amp capacitor C is connected to the feedback circuit. This type of controller is characterized by a time constant T.

A proportional-integral controller (PI controller) is implemented by connecting a resistor with resistance Roc and a capacitor Coc to the op-amp feedback circuit. Such a regulator is characterized by the following parameters: proportionality coefficient To and time constant T.

For all types of regulators, the implementation circuit has an input resistance R 1.

Schemes for implementing regulators, the dependence of the voltage at the regulator output U out on the input U in and their graphical representation, as well as formulas for finding the parameters of the regulators are given in Table 1

Table 1 - Regulators

Explain what current sensors are intended for and what requirements apply to them. Provide functional diagrams of a DC electric drive with a transformer current sensor and a shunt-based current sensor.

Current sensors (CT) are designed to obtain information about the strength and direction of the motor current. They are subject to the following requirements:

Linearity of control characteristics in the range from 0.1I nom to 5I nom not less than 0.9;

Availability of galvanic isolation of the power circuit and control system;

High performance.

The AEP coordinate sensor can be structurally represented as a serial connection of a measuring transducer (MT) and a matching device (CU) (Figure 1). The measuring transducer converts the coordinate X in electrical voltage signal And(or current i), proportional X. The matching device converts the output signal And IP into the feedback signal u os, which in size and shape satisfies the ACS.

Figure 1 – Block diagram of the AEP coordinate sensor

Current transformers, additional (compensation) windings of smoothing chokes, Hall elements, and shunts are used as measuring transducers in DT.

Current sensors based on shunts are widely used for measuring motor current. Shunt is a four-terminal resistor with purely active resistance R w(non-inductive shunt), the power circuit is connected to the current terminals, and the measuring circuit is connected to the potential terminals. (Figure 2)

To reduce the effect of the shunt on the passage of current in the motor circuit, its resistance should be minimal. The nominal voltage drop across the shunt is usually 75 mV, so it must be amplified using an amplifier. Since the shunt has a potential connection to the power circuit, the current sensor must contain a galvanic isolation device (GID). Transformer and optoelectronic devices are used as such devices.

Figure 2 – Circuit diagram for connecting a current sensor based on a shunt

DTs based on current transformers are mainly used in DC AEDs to measure the current of motors when they are powered by symmetrical bridge single-phase and three-phase rectifiers. For a single-phase rectifier (Figure 3), one current transformer (TA1) is used, and for a three-phase rectifier, three transformers connected to a star are used. To ensure the operating mode of current transformers is close to the short circuit mode, their secondary windings are loaded with low-resistance resistors R CT (0.2...1.0 Ohm). The conversion of alternating voltage of the secondary windings is carried out by the rectifier VD1...VD4.

Figure 2 – Circuit diagram for connecting a current sensor based on a current transformer

13. Provide a functional diagram of the armature EMF sensor, explain the principle of its operation.

With low requirements for the speed control range (up to 50), EMF feedback is used as the main feedback in the electric drive. The principle of operation of the armature EMF sensor is based on calculating the EMF of the motor.

The functional diagram of the EMF sensor is shown in Figure 1.

Figure 1 – Functional diagram of the armature EMF sensor

To measure the armature voltage, a divider is used on resistors R2, R3. To measure the motor armature current, an additional winding L1.2 of the smoothing choke is used. Voltage and I through a divider, RC filter and repeater A1 is fed to adder A2. A signal proportional to the voltage drop across the armature winding is also supplied to the input of adder A2 R i. ts ∙i i.

Output voltage expression u de amplifier A2 for steady-state operation has the form

Where To de – transmission coefficient of the EMF sensor,

e I is the armature emf.

To obtain a signal proportional to the voltage at the motor armature, a resistive voltage divider can also be connected according to the following circuit

Figure 2 – Voltage sensor connection diagram

The output voltage of the divider is

In addition to the divider, the voltage sensor may also contain galvanic isolation devices and

amplifier.

14. Draw a diagram of a vertical single-channel pulse-phase control system, explain the principle of its operation using timing diagrams.

To control the rectifier thyristors, a pulse-phase control system (PPCS) is used, which performs the following functions:

Determining the moments at which certain specific thyristors should open; these moments of time are set by a control signal that comes from the output of the ACS to the input of the SIFU;

Formation of opening pulses transmitted at the required times to the control electrodes of the thyristors and having the required amplitude, power and duration.

Let's consider the operation of a vertical single-channel SIFU controlling the thyristors of a single-phase bridge rectifier (Figure 1).

Figure 1 – Diagram of a single-phase bridge rectifier

The alternating voltage generator GPN starts when voltage C is received from the synchronizer (Figure 2). This happens at the moment when direct voltage is applied to the thyristors, i.e. at natural commutation points.

Figure 2 – Scheme of a vertical single-channel SIFU

From the output of the GPG, the sawtooth voltage is supplied to the comparison device US, where it is compared with the control voltage U y (Figure 3). At the moment of equality of the sawtooth and control voltages, the control unit generates a pulse, which is sent through the pulse distributor RI to the pulse shaper FI1 or FI2 and then through the output shaper VF1 or VF2 to the rectifier thyristors. The output shapers amplify the opening pulses in power and potentially separate the SIFU from the power section. A comparator based on an operational amplifier is used as a comparator.

Figure 3 – SIFU operation diagrams

15. Give a functional diagram of an electric drive with a three-phase zero reversible rectifier with joint control and explain the principle of its operation.

When controlling sets of thyristors together, opening pulses are simultaneously applied to both sets VS1, VS2, VS3 and VS4, VS5, VS6 (Figure 1). At the same time, depending on the direction of rotation of the engine, one set operates in rectifier mode, and the other in inverter mode. The armature current flows through the set operating in rectifier mode.

Figure 1 – Joint control of sets of three-phase zero valves

reversing rectifier

The rectifier thyristor control system contains two SIFU (SIFU1, SIFU2) and an analog inverter A1.

If VS1, VS2, VS3 operate in rectifier mode, and VS4, VS5, VS6 in inverter mode, then the motor rotates forward. If it's the other way around, the engine rotates backwards.

Since opening pulses are applied to both sets, a closed circuit of two phases of the secondary winding of transformer TV1 is formed in the circuit through two open valves, for example VS1 and VS6.

In this circuit, the sum of the EMF of the two phases of the secondary winding acts, which is called equalizing EMF:

Where e 1 , e 2 - rectified EMF of sets VS1...VS3 and VS4...VS6, respectively.

Equalizing EMF e ur creates equalizing current level 1. In relation to the equalizing current, transformer TV1 is in short circuit mode, because the active and inductive resistance of the transformer are small. Therefore, to limit the equalizing current, equalizing reactors L1 and L2 are included in its flow circuit.

In addition to the inclusion of equalizing reactors, limiting the equalizing current is achieved by coordinated control of the sets, in which the constant component of the equalizing EMF E ur is equal to zero, i.e.

E ur = E 1 + E 2 = E 0 (cosα 1 +cosα 2) = 0, (1)

Where E 1, E 2- constant components of EMF e 1 and e 2 respectively; E 0- constant component of the rectified emf at α = 0; α 1, α 2 - opening angles of sets VS1...VS3 and VS4...VS6.

Condition (1) will be satisfied when a 1 + a 2 =p. This condition is a condition for coordinated control of sets of thyristors.

Collaborative management has the following advantages:

· Equalizing currents ensure the conducting state of both sets, regardless of the magnitude of the motor load current and, as a result, the linearity of the characteristics (there is no intermittent current mode).

· High performance due to constant readiness for current reversal, which is not associated with any switching in the circuit.

However, with joint control it is necessary to install equalizing reactors, which increases the weight, cost and dimensions of the electric drive. The flow of equalizing currents increases the load on the power circuit elements and reduces the efficiency of the rectifier.

16. Draw a block diagram of an electric drive with a reversible rectifier with separate control and explain the principle of its operation.

In a reversible rectifier with separate control, when one set of thyristors is operating in rectifier or inverter mode, the other set is completely disabled (opening pulses are removed). As a result, there is no equalizing current circuit, which eliminates the need for equalizing reactors.

The block diagram of an electric drive with a reversible rectifier with separate control (RSRU) is shown in Figure 1. The operation of the RSRU is ensured by additional elements of the thyristor control system: valve conductivity sensor (VCS), logical switching device (LSD), characteristic switch (CH).

Figure 1 – Block diagram of an electric drive with a reversible rectifier

with separate control

The DPV is designed to determine the state (open or closed) of the rectifier thyristors and generate a signal about their blocking, which is equivalent to the absence of current in the sets.

The health care facility performs the following functions:

Selects the required set of valves “Forward” or “Backward” (KV “V” or KV “N”) depending on the required direction of the motor current, specified by the signal U 3

Prohibits the appearance of opening pulses simultaneously in both sets of thyristors using the “Forward” (“B”) and “Backward” (“H”) keys;

Prohibits the supply of opening pulses to the set that is coming into operation as long as current flows in the previously operating set;

Forms a temporary pause between the moment of closing of all thyristors of the previously operating set and the moment of supplying opening pulses to the set that is starting to operate.

The characteristic switch serves to match the unipolar adjustment characteristic of the SIFU α = ƒ(u у) with the reversing signal U у.

Reversing the motor begins with a change in the sign of the speed command, which causes a change in the sign of the current command Uc. This leads to a decrease in the control voltage U y, an increase in the opening angle α 1 of the thyristors of the “Forward” valve set, therefore, a decrease in the EMF E 1 and, ultimately, a decrease in the armature current to zero. The closing of the valves is recorded by the DPV. When receiving a signal from the DPV, the LPU prohibits the supply of pulses to the thyristors of both sets (“B” opens) and simultaneously begins to count the time pause. After its completion, the LPU generates permission to supply opening pulses to the thyristors of the “Back” valve set (the “H” is closed) and switch the PH. Switching the PC leads to a change in the polarity of the control voltage U at the input of the SIFU. From this moment, an opening pulse with an angle α 2 begins to be supplied to the HF “N”, ensuring the operation of the set in inverter mode. Since the rotational emf is greater than E 2, the armature current flows in the opposite direction. The engine switches to generator mode, performing regenerative braking.

Separate control has the following advantages:

There are no equalizing reactors, which significantly reduces the dimensions, weight and cost of the reversible rectifier;

There is no equalizing current, which reduces power losses in the rectifier and increases its efficiency.

The disadvantages of the split equation are:

The presence of an intermittent current mode, which requires linearization of the rectifier control characteristics;

A more complex management system due to the presence of health care facilities, long-term care facilities and mental hospital;

The presence of a dead pause when switching sets.

Give and describe closed structures of electronic devices built according to the principle of compensation of external disturbances and the principle of deviation. Draw a block diagram of a two-circuit slave control system for a DC electric drive and describe its blocks.

Closed structural EDs are built according to the principle of compensation of external disturbances and the principle of deviation, also called the feedback principle.

Let us consider the principle of compensation using the example of compensation for the most characteristic external disturbance of an electric drive - the load torque Mc when regulating its speed ω (Figure 1a).

Figure 1 – Closed structures of electronic structures

The main feature of such a closed structure of the electric drive is the presence of a circuit through which a signal proportional to the load torque is supplied to the input of the electric drive, together with the speed setting signal Usc

Um = Km∙Ms, where Km is the proportionality coefficient.

As a result, the electric drive is controlled by the total signal U ∆, which, automatically changing when the load torque fluctuates, ensures that the speed is maintained at a given level. Despite its effectiveness, electric drive control using this scheme is rarely carried out due to the lack of simple and reliable load torque sensors Ms.

Therefore, in most closed circuits the deflection principle is used, which is characterized by the presence of a feedback circuit connecting the output of the electronic device to its input. In this case, when regulating the speed, a speed feedback circuit is used (Figure 1b), through which information about the current speed value (signal Uos = Kos∙ ω) is supplied to the input of the electric drive, where it is subtracted from the speed setting signal Uss. Control is carried out by a deviation signal U ∆ =Uзс-Uос (it is also called a mismatch or error signal), which, when the speed differs from the set one, automatically changes accordingly and, with the help of an automatic control system, eliminates these deviations.

Depending on the type of controlled coordinate, the ED uses feedback in speed, position, current, magnetic flux, voltage, and EMF.

Subordinate regulation system.

To control the movement of the EUT, sometimes it is necessary to adjust several coordinates of the EP. For example, current (torque) and speed. In this case, closed EDs are performed according to a scheme with subordinate coordinate control.

Figure 2 – Block diagram of a two-circuit slave control system

In this scheme, the regulation of each coordinate is carried out by its own regulators (current RT and speed RS), which, together with the corresponding feedbacks with the coefficients Kost and Koss, form closed loops. These circuits are arranged in such a way that the input (master) signal for the current circuit Uzt is the output signal of the speed circuit external to it. Thus, the internal current loop will be subordinated to the external speed loop - the main adjustable coordinate of the electric drive. The U ∆ signal from the RT output is supplied to the thyristor converter TP. The electric motor is represented by two parts: electrical (ESM) and mechanical (MCD).

The main advantage of such a scheme is the possibility of optimal adjustment of the control of each coordinate. In addition, subordinating the current loop to the speed loop makes it possible to simplify the process of limiting current and torque, for which it is only necessary to maintain the signal at the output of the speed controller (reference signal) of the current level at the appropriate level.

Explain what static frequency converters with an intermediate direct current link (SFC IDC) are intended for. Give block diagrams of the PZPT HRC, which differ in the method of regulating the voltage on the IM stator.

HRC PZPT are designed to convert alternating voltage with constant amplitude and frequency into alternating voltage with adjustable amplitude and frequency.

There are three types of HRC CRPT depending on the method of voltage regulation:

1. HRC PZPT with a controlled rectifier

In this circuit, the voltage amplitude is regulated at the output of the rectifier (Figure 1).

Figure 1 - HRC PZPT with a controlled rectifier

CF is a controlled rectifier that converts alternating current energy into direct current energy.

F – filter, serves to smooth out current and voltage ripples.

And – inverter, used to convert direct current into alternating current.

SUV – rectifier control system.

IMS – inverter control system.

FP is a functional converter, used to convert the frequency setting signal U z. f. into the voltage setting signal U z. u. depending on the implemented frequency control law.

Depending on the type of filter F in the DC link, the autonomous inverter I is divided into current AI and voltage AI. In an IFC based on AI current, the filter is a reactor L with high inductance (Figure 2a). Such an inverter is a source of current, therefore, in this circuit, the control effect on the motor is the frequency and stator current.

Figure 2 - Filter circuits

The voltage AI is a voltage source, for which purpose the filter, in addition to the inductance L, contains a large capacitance capacitor C (Figure 2b). The control influence on the motor in the VHF system with AI voltage is the amplitude and frequency of the voltage.

2. HRC PZPT with an uncontrolled rectifier and a pulse-width controlled converter (PWCC) in the DC link (Figure 3).

Figure 3 - HRC PZPT with an uncontrolled rectifier and PSIU

In this case, voltage regulation is carried out in the PShIU, which is installed between the uncontrolled rectifier NV and the inverter I. The unregulated constant voltage from the NV is supplied to the PShIU, where it is regulated in magnitude, converted into a sequence of rectangular pulses, filtered by filter Ф and supplied to the input of the inverter I.

3. HRC PZPT with an uncontrolled rectifier and with pulse-width modulation of the voltage in the inverter (Figure 4).

Figure 4 - PFC DCPT with pulse-width modulation of voltage in the inverter

In this circuit, regulation of voltage amplitude and frequency is combined in I. Pulse width modulation is achieved using a complex valve switching algorithm and can only be implemented in converters with controlled switches: with power transistors or with thyristors with artificial switching.

The advantage of PWM controllers using operational amplifiers is that almost any op-amp can be used (in a typical switching circuit, of course).

The level of the output effective voltage is regulated by changing the voltage level at the non-inverting input of the op-amp, which allows the circuit to be used as an integral part of various voltage and current regulators, as well as circuits with soft ignition and extinguishing of incandescent lamps.
Scheme it is easy to repeat, does not contain rare elements, and if the elements are in good working order, it starts working immediately, without configuration. The power field-effect transistor is selected according to the load current, but to reduce thermal power dissipation it is advisable to use transistors designed for high current, because they have the least resistance when open.
The radiator area for a field-effect transistor is completely determined by the choice of its type and the load current. If the circuit will be used to regulate the voltage in on-board networks + 24V, to prevent breakdown of the gate of the field-effect transistor, between the collector of the transistor VT1 and shutter VT2 you should turn on a resistor with a resistance of 1 K, and the resistor R6 shunt with any suitable 15 V zener diode, the remaining elements of the circuit do not change.

In all previously discussed circuits, a power field-effect transistor is used n- channel transistors, as the most common and having the best characteristics.

If it is necessary to regulate the voltage on a load, one of the terminals of which is connected to ground, then circuits are used in which n- The channel field-effect transistor is connected as a drain to + of the power source, and the load is switched on in the source circuit.

To ensure the possibility of fully opening the field-effect transistor, the control circuit must contain a unit for increasing the voltage in the gate control circuits to 27 - 30 V, as is done in specialized microcircuits U 6 080B ... U6084B, L9610, L9611 , then between the gate and source there will be a voltage of at least 15 V. If the load current does not exceed 10A, you can use power field p - channel transistors, the range of which is much narrower due to technological reasons. The type of transistor in the circuit also changes VT1 , and the adjustment characteristic R7 reverses. If in the first circuit an increase in the control voltage (the variable resistor slider moves to the “+” of the power source) causes a decrease in the output voltage at the load, then in the second circuit this relationship is the opposite. If a specific circuit requires an inverse dependence of the output voltage on the input voltage from the original one, then the structure of the transistors in the circuits must be changed VT1, i.e. transistor VT1 in the first circuit you need to connect as VT1 for the second scheme and vice versa.

The main types of regulators used in control systems for electric drives of drilling rig actuators

Analog regulators in slave control systems for electric drives are built on the basis of operational amplifiers (op-amps) - direct current amplifiers with high input and very low output impedances. Integrated circuit technology now makes it possible to produce high-quality and inexpensive op-amps. In some part of its operating range, the op-amp behaves like a linear voltage amplifier with a very high gain (10 5 - 10 6). If the op-amp circuit does not provide negative feedback from the output to the input, then due to the high gain, it will necessarily fall into saturation mode. Therefore, op-amp based regulator circuits contain negative feedback.
The operational amplifier gets its name from the fact that it can perform various mathematical operations such as multiplication, summation, integration and differentiation. Typical regulators are built on the basis of an inverting amplifier, and the input and output circuits, in addition to resistances, may contain capacitors.
Since the op-amp gain is large (Ku= = 10 5 +10 6), and the output voltage Uvy is limited by the supply voltage CPU, then the potential of the point A(Fig. 1, a) cpA = = uout/Ku is close to zero, i.e. dot A performs the function of apparent ground (ground the point A it is impossible, otherwise the circuit will become inoperative).

Rice. 1. The structure of an analog regulator made on an operational amplifier (a). Circuit of a proportional controller with controlled limitation of the output signal (b). Characteristics of the input-output regulator with controlled limitation of the output signal (c)

Circuits, transfer functions and transition functions of various types of regulators are given in table.

Circuits and dynamic characteristics of various types of regulators

To obtain a proportional controller (P-regulator), resistors are included at the input and in the feedback circuit of the op-amp; The integral regulator (I-regulator) includes a resistor in the input circuit, and a capacitor in the feedback circuit; The PI controller contains a resistor in the input circuit, and a series-connected resistor and capacitor in the feedback circuit. The PID controller can be implemented on a single amplifier using active-capacitive circuits at the input and in the feedback circuit.
The industry produces various types of operational amplifiers on integrated circuits (ICs) - both round and rectangular. The most widely used types of op-amps for constructing regulators are K140UD7, K553UD2, K157UD2, etc.
It is possible to reduce the size and increase the reliability of devices of analog control systems for electric drives by introducing hybrid technology for their manufacture. In the manufacture of hybrid integrated circuits (HICs), active elements (OA) are installed on a printed circuit board in a solid-state (unpackaged) design, and capacitors and resistors are installed using the film technology method (by sputtering films of conductive, semiconducting and non-conducting materials). The resulting module can be filled with compound or placed in a housing.
Limitation of the coordinates of the electric drive (current, speed, etc.) is carried out by including limiting units in the structure of the regulator of the external control loop. The latter can be controlled or uncontrollable. In Fig., 6 shows a circuit for limiting the output voltage of a proportional regulator with cut-off diodes VD1, VD2 and a controlled reference voltage Vop. The circuit allows you to obtain an input-output characteristic that is asymmetrical relative to the origin of coordinates with different levels of limited output voltage (Fig.) Other options for controllable limiting circuits of op-amp output voltage using transistors are also possible.
Until recently, in the automated electric drive of actuators of domestic drilling rigs, analog computer technology was mainly used. In recent years, a number of design and research organizations have been working on the creation of microprocessor control systems. Compared to analog systems, microprocessor systems have a number of advantages. Let's note some of them.
Flexibility. The ability, by reprogramming, to change not only the parameters of the control system, but also the algorithms and even the structure. At the same time, the hardware of the system remains unchanged. In analog systems, the hardware would have to be re-arranged. Microcomputer software can be easily adjusted both during the pre-launch period and during their operation. Thanks to this, the costs and timing of adjustment work are reduced and their nature changes, since the necessary experiments to determine characteristics and parameters, as well as setting up regulators, can be carried out automatically by the microcomputer itself using a pre-prepared program.
Removing all restrictions on the structure of the control device and control laws. At the same time, the quality indicators of digital systems can significantly exceed the management quality indicators of continuous control systems. By introducing appropriate programs, complex control laws (optimization, adaptation, forecasting, etc.) can be implemented, including those that are very difficult to implement using analogue means. It becomes possible to solve intellectual problems that ensure the correctness and efficiency of technological processes. Systems of any type can be built on the basis of a microcomputer, including systems with subordinate control, multidimensional systems with cross connections, etc.
Self-diagnosis and self-testing digital control devices. The ability to check the serviceability of mechanical drive components, power converters, sensors and other equipment during process breaks, i.e. automatic diagnostics of equipment condition and early warning of accidents. These capabilities are complemented by advanced anti-interference capabilities. The main thing here is the replacement of analog information transmission lines with digital ones containing galvanic isolation, fiber-optic channels, and noise-resistant integrated circuits as amplifiers and switches.
Higher accuracy due to the absence of zero drift, characteristic of analog devices. Thus, digital electric drive speed control systems can provide an increase in control accuracy by two orders of magnitude compared to analogue ones.
Easy to visualize parameters of the control process through the use of digital indicators, indicator panels and displays, organizing an interactive mode of information exchange with the operator.
Greater reliability, smaller dimensions, weight and cost. The high reliability of microcomputers compared to analog technology is ensured by the use of large integrated circuits (LSIs), the presence of special memory protection systems, noise immunity and other means. Thanks to the high level of LSI production technology, the costs of manufacturing electric drive control systems are reduced. These advantages are especially evident when using single-board and single-chip computers.

The controller calculates the mismatch and converts it into a control action in accordance with a certain mathematical operation. VSAU mainly uses the following types of controllers: proportional (P), integral (I), proportional-integral (PI), proportional-integral-derivative (PID). Depending on the type of converted signals, analogue and digital regulators are distinguished. Analog regulators (AR) are implemented based on operational amplifiers, digital - based on specialized computing devices or microprocessors. Analog controllers only convert analog signals that are continuous functions of time. When passing through the AP, each instantaneous value of a continuous signal is converted.

When analyzing regulators, we will use two main assumptions, which are met with a high degree of accuracy for an op-amp with negative feedback in a linear operating mode:

Differential input voltage U op-amp input is equal to zero;

The inverting and non-inverting inputs of the op-amp do not consume current, i.e. input currents (Fig. 2.2). Since the non-inverting input is connected to the “zero” bus, then, according to the first assumption, the potential φa of the inverting input is also zero.

Rice. 2.2. Functional diagram of a proportional controller

Moving on to the increment of variables in equation (2.1) and using the Laplace transform, we obtain the transfer function of the P-regulator:

Where - proportional gain.

Thus, in the P-regulator, a proportional amplification (multiplying by a constant) of the error signal is carried out u race

The coefficient can be either greater or less than one. In Fig. 2.3 shows the dependence u at = f(t) P-regulator when the error signal changes u race

An integral regulator (I-regulator) is implemented by connecting an op-amp capacitor C to the op-amp in the feedback circuit (Fig. 2.4). Transfer function of the I controller

where is the constant of integration, s.

Rice. 2.4. Functional diagram of an integrated regulator

The I controller integrates the error signal u race

A proportional-integral controller (PI controller) is implemented by including a resistor R OU and a capacitor C OU in the feedback loop (Fig. 2.6).

Rice. 2.6. Functional diagram of the PI controller

Transfer function of the PI controller

is the sum of the transfer functions of the proportional and integral controllers. Since the PI controller has the properties of P and I controllers, it simultaneously performs proportional amplification and integration of the error signal u race

A proportional-integral-derivative controller (PID controller) is implemented in the simplest case by connecting capacitors C 3 and C OS in the PI controller in parallel with resistors R 3 and R OC (Fig. 2.8).

Rice. 2.8. Functional diagram of the PID controller

PID controller transfer function

where is the proportional gain of the PID controller; - constant of differentiation; - integration constant; ; .

The transfer function of the PID controller is the sum of the transfer functions of the proportional, integral and differential controllers. The PID controller performs simultaneous proportional amplification, differentiation and integration of the error signal u race

17 Question AEP coordinate sensors.

Block diagram of the sensor. The AED (automated electric drive) uses sensors to receive feedback signals on controlled coordinates. Sensor is a device that informs about the state of the controlled coordinate of the AED by interacting with it and converting the reaction to this interaction into an electrical signal.

Controlled in the AED are electrical and mechanical coordinates: current, voltage, EMF, torque, speed, displacement, etc. To measure them, appropriate sensors are used.

The AED coordinate sensor can be structurally represented as a serial connection of a measuring transducer (MT) and a matching device (CU) (Fig. 2.9). The measuring transducer converts the coordinate X in electrical voltage signal And(or current i), proportional X . The matching device converts the output signal And IP into feedback signal u OS , which in size and shape satisfies the self-propelled guns.

Rice. 2.9. Block diagram of the AEP coordinate sensor

Current sensors. Current sensors (CT) are designed to obtain information about the strength and direction of the motor current. They are subject to the following requirements:

Linearity of control characteristics in the range from 0.1I nom to 5 I nom not less than 0.9;

Availability of galvanic isolation of the power circuit and control system;

High performance.

Current transformers, additional (compensation) windings of smoothing chokes, Hall elements, and shunts are used as measuring transducers in DT.

Current sensors based on shunts are widely used for measuring motor current. Shunt is a four-terminal resistor with purely active resistance R sh (non-inductive shunt), the power circuit is connected to the current terminals, and the measuring circuit is connected to the potential terminals.

According to Ohm's law, the voltage drop across the active resistance and=R w i.

To reduce the effect of the shunt on the passage of current in the motor circuit, its resistance should be minimal. The nominal voltage drop across the shunt is usually 75 mV, so it must be amplified to the required values (3.0...3.5 V). Since the shunt has a potential connection with the power circuit, the current sensor must contain a galvanic isolation device. Transformer and optoelectronic devices are used as such devices. The block diagram of a current sensor based on a shunt is shown in Fig. 2.13.

Rice. 2.13. Block diagram of a shunt-based current sensor

Currently, current sensors based on Hall elements, which are made of semiconductor material in the form of a thin plate or film (Fig. 2.14). When an electric current I X passes through a plate located perpendicular to a magnetic field with induction IN, Hall emf is induced in the plate e X:

where is a coefficient depending on the properties of the material and the dimensions of the plate.

Voltage sensors. IN Resistive voltage dividers are used as a voltage measuring converter in an electric drive (Fig. 2.16).

Rice. 2.16. Functional diagram of a voltage sensor

Divider output voltage.

EMF sensors. With low requirements for the speed control range (up to 50), EMF feedback is used as the main feedback in the electric drive.

Rice. 2.17. Functional diagram of the armature EMF sensor

Speed sensors. To obtain an electrical signal proportional to the angular velocity of the engine rotor, tachogenerators and pulse speed sensors are used. Tachogenerators are used in analog automatic control systems, pulse ones - in digital ones.

Speed sensors are subject to strict requirements for the linearity of the control characteristics, the stability of the output voltage and the level of its ripple, since they determine the static and dynamic parameters of the drive as a whole.

DC tachogenerators with permanent magnets have become widespread in electric drives. To reduce the level of reverse pulsations, tachogenerators are built into the electric motor.

In pulsed speed sensors, pulsed displacement transducers are used as the primary measuring transducer, in which the number of pulses is proportional to the angle of rotation of the shaft.

Position sensors. IN Currently, induction and photoelectronic converters are used in electric drives to measure the movement of moving parts of machines and mechanisms.

Induction transformers include rotating transformers, selsyns and inductosyns. Inductosyns can be circular or linear.

Rotating transformers (VT) are called electrical micromachines of alternating current that convert the angle of rotation α into a sinusoidal voltage proportional to this angle. In an automatic control system, rotating transformers are used as mismatch meters that record the deviation of the system from a certain specified position.

A rotating transformer has two identical single-phase distributed windings on the stator and rotor, shifted by 90° to each other. The voltage from the rotor winding is removed using slip rings and brushes or using ring transformers.

The operating principle of the VT in sinus mode is based on the dependence of the voltage induced in the rotor winding by the pulsating magnetic flux of the stator on the angular position of the axes of the stator and rotor windings.

Selsin is an alternating current electric micromachine with two windings: excitation and synchronization. Depending on the number of phases of the excitation winding, single- and three-phase synchros are distinguished. The synchronization winding is always three-phase. In self-propelled guns, non-contact synchros with a ring transformer are widely used.

The synchronization winding of a non-contact synchronizer with a ring transformer is located in the slots of the stator, the excitation winding is in the slots or on the pronounced poles of the rotor of the synchronizer. The peculiarity of the ring transformer is that its primary winding is located on the stator, and the secondary winding is located on the rotor. The windings have the form of rings placed in a magnetic system consisting of ring magnetic cores of the stator and rotor, which are connected on the rotor by an internal magnetic circuit, and on the stator by an external one. In self-propelled guns, synchros are used in amplitude and phase rotation modes.

The circuit diagram for switching on the synsyn windings in amplitude mode is shown in Fig. 2.19. The input coordinate of the synchronizer in this mode is the rotor rotation angle τ. The center line of the phase winding is taken as the reference point A.

Rice. 2.19. Functional diagram of switching on the synsyn windings in amplitude mode

The circuit diagram for switching on the synsyn windings in the phase-shift mode is shown in Fig. 2.20. The input coordinate of the synchronizer in this mode is the rotation angle τ, and the output coordinate is the phase φ of the output EMF e out in relation to the alternating supply voltage.

Rice. 2.20. Functional diagram of switching on the synsyn windings in phase rotation mode

18 Question Pulse-phase control systems. Principles of thyristor control.

In rectifiers, thyristors are used as controlled switches. To open the thyristor, two conditions must be met:

The anode potential must exceed the cathode potential;

An opening (control) pulse must be applied to the control electrode.

The moment a positive voltage appears between the anode and cathode of the thyristor is called moment of natural opening. The supply of the opening impulse can be delayed relative to the moment of natural opening by an opening angle. As a result, the onset of current flow through the thyristor entering operation is delayed and the rectifier voltage is regulated.

To control the rectifier thyristors, a pulse-phase control system (PPCS) is used, which performs the following functions:

Determining the moments at which certain specific thyristors should open; these moments of time are set by a control signal that comes from the output of the ACS to the input of the SIFU;

Formation of opening pulses transmitted I at the right times to the control electrodes of the thyristors and having the required amplitude, power and duration.

According to the method of obtaining a shift of opening pulses relative to the point of natural opening, horizontal, vertical and integrating control principles are distinguished.

With horizontal control (Fig. 2.28), the control alternating sinusoidal voltage u y is out of phase (horizontally) with respect to voltage u 1, feeding the rectifier. At a moment in time ωt=α Rectangular unlocking pulses are formed from the control voltage U GT . Horizontal control is practically not used in electric drives, which is due to the limited range of angle control α (about 120°).

With vertical control (Fig. 2.29), the moment of supply of opening pulses is determined when the control voltage is equal u y (constant in shape) with a variable reference voltage (vertical). At the moment of voltage equality, rectangular pulses are formed U gt.

With integrating control (Fig. 2.30), the moment of supply of opening pulses is determined when the alternating control voltage is equal and at with constant reference voltage U o p. At the moment of voltage equality, rectangular pulses are formed U gt.

Rice. 2.28. Horizontal control principle

Rice. 2.29. Vertical control principle

Rice. 2.30. Integrating control principle

According to the method of counting the opening angle a, SIFUs are divided into multi-channel and single-channel. In multi-channel SIFUs, the angle a for each rectifier thyristor is measured in its own channel, in single-channel ones - in one channel for all thyristors. In industrial electric drives, multichannel SIFUs with a vertical control principle are predominantly used.

TYPICAL DEVICES OF CONTROL SYSTEMS

Regulators

An important function of modern automation systems is the regulation of its coordinates, that is, maintaining the required values with the necessary accuracy. This function is implemented using a large number of different elements, among which regulators are of paramount importance.

Regulator performs transformation of the control signal corresponding to the mathematical operations required by the operating conditions of the control system. Typical required operations include the following signal transformations: proportional, proportional-integral, proportional-integral-differential.

The basis of the analog regulator is an operational amplifier - a direct current amplifier, which, in the absence of feedback, has a high gain. Integrated operational amplifiers are most widely used. An operational amplifier is a multistage structure in which one can distinguish an input differential amplifier ( DU) with inverse and direct inputs, voltage amplifier ( UN), implementing high gain, and a power amplifier ( MIND), providing the necessary load capacity of the operational amplifier. The functional diagram of the operational amplifier is shown in Fig. 4.1. The single-chip, small-sized design of the operational amplifier ensures high stability of the parameters, which makes it possible to obtain a high DC gain. Points derived from the diagram Kl, K2, KZ designed for connecting external correction circuits that reduce the gain at high frequencies and increase the stability of the amplifier with feedback. Without correction circuits, at sufficiently high frequencies, when the accumulated phase lag is 180°, the sign of the feedback changes, and with a large gain, the operational amplifier self-excites and enters the self-oscillation mode. In Fig. 4.1 the following notations are used: U p- amplifier supply voltage; U ui- input control voltage via the inverse input of the amplifier; U pack- input control voltage via direct input of the amplifier; U out- amplifier output voltage. All of the above voltages are measured relative to the common wire of a bipolar power supply.

The operational amplifier connection circuits are shown in Fig. 4.2. The differential stage of the operational amplifier has two control inputs: direct with potential U pack and inverse with potential U ui(Fig. 4.2, A).

The output voltage of the amplifier is determined by the product of the gain and the potential difference of the amplifier inputs, that is

U out = k уо (U up - U уу) = k уо U у,

Where k uo- differential gain of the operational amplifier; U y- differential input voltage of the amplifier, that is, the voltage between the direct and inverse inputs. Differential gain of integrated operational amplifiers in the absence of feedback.

Relative to input voltages U vhp And U whi output voltage is determined by the difference

U out = k up U in - k ui U in,

where are the direct input gains k pack and by inverse input k ui determined by the amplifier switching circuit. For the direct input switching circuit shown in Fig. 4.3, b, the gain is determined by the formula

and for the inverse input switching circuit shown in Fig. 4.3, V, - according to the formula

To build various regulator circuits, an operational amplifier circuit with an inverse input is usually used. Typically, regulators must have multiple inputs. Input signals are supplied to point 1 (Fig. 4.2, V) through individual input resistances. The required transfer functions of the regulators are obtained due to complex active-capacitive resistances in the feedback circuit Z os and in input circuits Z in. Transfer function of the regulator relative to any of the inputs without taking into account the inversion of the output voltage

. (4.1)

Depending on the type of transfer function, the operational amplifier can be considered as one or another functional regulator. In the future, to implement regulators, we will consider only switching circuits based on the inverse input.

Proportional controller (P-controller) - This is the tight feedback op amp shown in Fig. 4.3, A. Its transfer function

W(p) = k P, (4.2)

Where k P- gain coefficient of the P-regulator.

As follows from the transfer function (4.2), within the bandwidth of the operational amplifier, the logarithmic amplitude frequency response (LAFC) of the P-regulator is parallel to the frequency axis w, and the phase is zero (Fig. 4.3, b).

Integral controller (I-regulator) is obtained by including a capacitor in the feedback loop, as shown in Fig. 4.4, A, while integrating the input signal and the transfer function of the controller

, (4.3)

Where T and = R in C os- constant of integration.

As follows from (4.3), the phase shift of the output signal is equal to - p/ 2, the LFC has a slope of -20 dB/dec, and the logarithmic phase frequency response (LPFR) is parallel to the frequency axis w(Fig. 4.4, b).

Proportional-integral controller (PI controller ) is obtained by parallel connection of P- and I-regulators, that is

The transfer function (4.4) can be obtained on one operational amplifier by including active-capacitive reactance in its feedback Z os (p) = R os (p) + + 1 / (C os p), as shown in Fig. 4.5, A.

Then, in accordance with (4.1)

Where T 1 = R os C os; T I = R in C os; k P = R os / R in.

The logarithmic frequency characteristics of the PI controller are shown in Fig. 4.5, b.

Proportional differential controller (PD controller) is obtained by parallel connection of a P-regulator and a differential D-regulator, that is

W PD (p) = k P + T D p = k P (T 1 p+1). (4.5)

The transfer function (4.5) is obtained by connecting a capacitor to the input resistor of the op-amp, as shown in Fig. 4.6, A. Then, taking (4.1) into account, we have

Where T 1 = R in C in; k P = R os / R in.

The logarithmic frequency characteristics of the PD controller are shown in Fig. 4.6, b.

Proportional-integral-derivative controller (PID controller). This regulator is obtained by parallel connection of three regulators - P-regulator, I-regulator and D-regulator. Its transfer function has the form

. (4.6)

Transfer function (4.6) can always be implemented by parallel connection of a PD controller and an I controller, which have, respectively, transfer functions (4.5) and (4.3). In this case, the PID controller circuit can be implemented using three operational amplifiers. The first amplifier implements the function of a PD regulator (Fig. 4.6, A), the second amplifier is the function of the I-regulator (Fig. 4.4, A), third amplifier (Fig. 4.3, A) is the function of summing the output signals of the first and second amplifiers.

If the parameters k P, T I And T D impose a restriction

then the transfer function (4.6) can be written as

, (4.7)

Where k P = (T 1 +T 2) / T I; T D = (T 1 T 2) / T I.

A PID controller with a transfer function (4.7) is a sequential connection of a PD controller and a PI controller and can be implemented on a single operational amplifier with resistance in the feedback circuit

Z os (p) = R os + 1/(C os p)

and resistance in the input circuit

In this case, the controller time constants T 1 = R in C in, T 2 =R os C os, T 0 =R in C os.

The PID controller circuit for one amplifier is shown in Fig. 4.7, A, and its logarithmic frequency characteristics in Fig. 4.7, b.

The considered circuits of the PD controller and PID controller have capacitors in the input circuits of the amplifier, which for high-frequency interference represent a resistance close to zero. To increase the stability of the regulators, you can connect an additional resistor with a small resistance (at least one order of magnitude less than the capacitance of the capacitor) in series with the capacitor.

Regulators, their operation and technical implementations are discussed in more detail in /1/.

Self-test questions

1. What function do automation system regulators perform?

2. What typical transformations of the control signal are performed by regulators of automation systems?

3. What is the basis for the construction of most modern analog regulators?

4. What are the main properties of operational amplifiers?

5. What are the input coordinates of a typical op amp?

6. What is the output coordinate of a typical op amp?

7. What are the components included in the functional circuit of an operational amplifier?

8. Name typical circuits for connecting operational amplifiers.

9. What typical operational amplifier circuit is usually used to implement regulators?

10. Give the transfer function of the operational amplifier for the inverting input circuit.

11. Which element contains a proportional controller in the feedback circuit of an operational amplifier?

12. Which element contains a proportional controller in the input circuit of an operational amplifier?

13. Give the transfer function of a proportional controller.

14. What are the amplitude frequency and phase frequency characteristics of a proportional controller?

15. Which element contains an integral regulator in the feedback circuit of an operational amplifier?

16. Which element contains an integral regulator in the input circuit of an operational amplifier?

17. Give the transfer function of the integral regulator.

18. What is the slope of the logarithmic amplitude frequency response of an integral regulator?

19. What is the phase frequency response of an integral regulator?

20. What elements does the feedback circuit of an operational amplifier contain?

21. Which element contains the input circuit of the operational amplifier of the proportional-integral regulator?

22. Give the transfer function of a proportional-integral controller.

23. Which element contains the feedback circuit of the operational amplifier of the proportional differential regulator?

24. Give the transfer function of a proportional-differential controller.

25. Under what restrictions on the parameters of a proportional-integral-derivative controller is it implemented on a single operational amplifier?

26. What elements does the input circuit of a proportional-integral-derivative controller based on a single operational amplifier contain?

27. What elements does the feedback circuit of a proportional-integral-derivative controller based on a single operational amplifier contain?

Intensity controllers

A typical master unit in electric drive control systems and other automation systems is integrator or intensity controller(ZI). The task of the SI is to form a smooth change in the master signal when moving from one level to another, namely to create a linear rise and fall of the signal at the required rate. In steady state, the voltage at the intensity generator output is equal to the voltage at its input.

In Fig. Figure 4.8 shows a block diagram of a single-integrating SI, consisting of three operational amplifiers. All amplifiers are connected according to a circuit with an inverting input. First amplifier U1, operating without feedback, but with output voltage limitation U 1, has a rectangular characteristic, which is shown without taking into account the inversion of the output voltage in Fig. 4.9, A. Second operational amplifier U2 works as an integrator with a constant rate of integration

(4.8)

The rate of integration can be adjusted by changing Rin2. Third amplifier U3 generates negative feedback voltage

. (4.9)

When a reference voltage is applied to the input U z the output voltage increases linearly according to (4.8). At a moment in time t=t p, When U з = - U os, integration stops, and the output voltage, as follows from (4.9), reaches the value , remains unchanged further. When removing the setting voltage from the input ( U z = 0) the process of linear reduction of the output voltage to zero occurs (Fig. 4.9, b).

The rate of change of the output voltage of this protective device, as follows from (4.8), can change either by changing the voltage value U 1, for example, by selecting zener diodes in the amplifier feedback circuit U1 with stabilization voltage equal to the required value U 1, or by changing the value of the product R in2 C oc2.

In Fig. 4.10, A Shown is another circuit of a single-integrating SI, made on the basis of a bipolar transistor connected according to a circuit with a common base. This circuit uses the properties of a transistor ( T) as a current amplifier. Capacitor recharge ( WITH) always occurs at a constant collector current i to, determined by the given emitter current i e. In this case, the rate of change in voltage over time u out at the output of the ZI | duout/dt| = i to/C. Characteristics of ZI control u out = = f(t) shown in Fig. 4.10, b. The rate of change of the output signal can be adjusted by changing the voltage U e, in proportion to which the current changes i e and, accordingly, the current i to, or changing the capacitance of the capacitor. In steady state, the capacitor is always charged to voltage u in. The rectifier bridge ensures a constant direction of the transistor collector current, regardless of the sign of the voltage u in. ZI are discussed in detail in /1, 7/.

Self-test questions

1. For what purpose are intensity controllers used in automation circuits?

2. What are the input and output coordinates of the intensity generator?

3. What is the static gain of the intensity generator?

4. How should the voltage at the output of single-integrating intensity generators change with step changes in the input voltage?

5. On the basis of what amplifiers are integrating intensity controllers built?

6. How many operational amplifiers, connected via the inverse input, are needed to implement a one-time integrating intensity controller?

7. Indicate the purpose of each of the three operational amplifiers in a typical single-integrating intensity controller circuit made on microcircuits.

8. What parameters affect the rate of change of the output voltage of a single-integrating intensity generator on three operational amplifiers?

9. How is a linear change in the voltage across the capacitor achieved in the circuit of a single-integrating transistor intensity controller?

10. What parameters affect the rate of change of the output voltage of a single-integrating transistor intensity controller?

Matching elements

Functional elements within control systems can be heterogeneous in type of signal, type of current, resistance and power, and other indicators. Therefore, when connecting elements, the task of coordinating their characteristics arises. This problem is solved by matching elements. This group of elements includes phase detectors that match the type of current, digital-to-analog and analog-to-digital converters that match the type of signal, emitter followers, matching input and output resistances, power amplifiers, galvanic separators and other elements. The coordination function can also be performed by elements normally intended for other purposes. For example, the operational amplifier discussed in section 4.1 turns out to be an emitter follower relative to a non-inverting input when the output voltage is connected to the inverted input.

For galvanic separation, for example, a transformer voltage sensor can be used. Such and similar elements are obvious or known and will not be considered.

Let's consider more complex standard matching elements.

Phase detector(PD) has received a number of other names in the scientific and technical literature: phase-sensitive amplifier, phase-sensitive rectifier, phase discriminator, demodulator.

The purpose of the FD is to convert the input AC voltage U in V DC output voltage U out, the polarity and amplitude of which depend on the phase of the input voltage j. Thus, the PD has two input coordinates: the amplitude of the input voltage U in m and input voltage phase j and one output coordinate: the average value of the output voltage U out. There are two modes of PD operation: amplitude mode, when the phase of the input voltage remains constant, taking one of two values 0 or p, U in m= var and U out = f(U in m); phase mode when U in= const, j= var and U out = f(j).

In amplitude mode, the PD is used as a converter of an AC mismatch signal into a control signal in DC servo drives, as a converter of the output signal of an AC tachogenerator, and so on. In phase mode, PD is used in control systems in which the controlled and control variable is a smoothly varying phase.

The phase detector, as a rule, is not assigned the function of voltage amplification.

Therefore, the PD gain is close to unity. In Fig. Figure 4.11 shows the calculated equivalent circuit of a full-wave PD. The circuit corresponds to a zero rectification circuit, in which the valves are replaced by functional switches K1 And K2. Load resistance Rn, on which the output voltage is allocated, connects the midpoints A, 0 keys and sources of EMF control e y. The internal resistance of the control EMF source is introduced into each circuit R y. The state of the keys is controlled by the reference EMF e op in accordance with the algorithm: for e op > 0 K1 included, that is, it

switching function y k1= 1,a K2 disabled, that is, its switching function y k2 = 0. For e op< 0 y k1 = 0, A y k2= 1. This algorithm can be represented by the formulas

y to 1 = (1+sign e op) /2; y to 2 = (1- sign e op) /2 . (4.10)

Obviously, with closed K1 output emf e out between points A, 0 equal to e y, and when closed K2 e out = - e y, that is

e out = e y y k1 - e y y k2. (4.11)

Substituting (4.10) into (4.11) gives

e out = e y sign e op . (4.12)

The diagram of changes in the output EMF corresponding to algorithms (4.11) and (4.12) is shown in Figure 4.12.

e op = E op m sinwt And e y = E y m sin(wt - j),

Where E op m,E y m- amplitude values of the reference EMF and control EMF; w is the angular frequency of the reference EMF and the control EMF, then the average value of the rectified output EMF

. (4.13)

Because E y m = k p U in m, average output voltage , then taking into account (4.13)

, (4.14)

Where k p- transfer coefficient from the input voltage to the control EMF. It is determined by the features of a specific PD circuit diagram.

For j= const = 0 or j= const = p there is an amplitude mode of operation of the PD, for which the control characteristic is straightforward:

U out = k FD U in,

where, taking into account (4.14), the PD gain in the amplitude mode

At j= 0 output voltage values U out are positive, and when j = p output voltage values are negative.

For U in= const and j= var there is a phase mode of the PD, for which the control characteristic has the form

U out = k " FD cosj = k "FD sinj",

Where j " = p/2 - j, and the PD transmission coefficient in phase mode taking into account (4.14)

;

At small j" control characteristic

The operation of PDs, their characteristics and circuit diagrams are discussed in /1/.

Digital to Analogue Converters(DAC). The converter matches the digital part of the control system with the analog one. The input coordinate of the DAC is a binary multi-bit number A n = a n -1 …a i …a 1 a 0, and the output coordinate is voltage U out, generated based on the reference voltage U op(Fig. 4.13).

DAC circuits are built on the basis of a resistor matrix, with the help of which currents or voltages are summed so that the output voltage is proportional to the input number. The DAC consists of three main parts: a resistor matrix, electronic switches controlled by the input number, and a summing amplifier that generates the output voltage. In Fig. Figure 4.14 shows a simple circuit of an irreversible DAC. Each digit of the input binary number An corresponds to resistance

R i = R 0 / 2 i, (4.15)

Where R0- low-order resistance.

Resistor R i connects to a power supply with a reference voltage U op via electronic key K i, which is closed at a i=1 and open at a i= 0. Obviously, depending on the value a i input circuit resistance for i- th category taking into account (4.15) will be determined by the expression

R i = R 0 /(2 i a i). (4.16)

Then for and i= 0, that is, the circuit is broken, and for a i=1 circuit is on and has resistance R 0 /2 i .

In the diagram in Fig. 4.14 operational amplifier U sums the input currents and its output voltage, taking into account the circuit notation and expression (4.16)

Expression (4.17) of the form U out = f(A n)- This is the control characteristic of the DAC. It has a stepped shape with a voltage discreteness corresponding to the least significant unit,

ΔU 0 = R os U op / R 0 = k DAC.

Magnitude ΔU 0 is at the same time the average transfer coefficient of the DAC k DAC.

Analog-to-digital converter(ADC) solves the inverse problem - converts a continuous input voltage into a number, for example, binary. Each output multi-bit binary number A i corresponds to the range of input voltage changes:

, (4.18)

Where U ei = ΔU 0 i- reference value of the output voltage corresponding to the output binary number A i; ΔU 0- discreteness of the output voltage, corresponding to the unit of the least significant digit of the output number.

At n-bit ADC, the total number of non-zero reference input voltage levels that differ from each other by ΔU 0, equal to the maximum output decimal number N=2 n - 1. Since each level U e i, according to (4.18), carries information about the number, then in the operation of the ADC we can distinguish the main operations: comparison of the input and reference voltages, determination of the level number, generation of the output number in a given code. The average ADC gain is defined as the reciprocal of the corresponding DAC gain:

k ADC = 1 / ΔU 0.

Then the equation for the ADC control characteristic can be written as

The ADC control characteristic has a step form.

ADC implementation circuits can be divided into two main types: parallel action and sequential action.

The main advantage of a parallel ADC is its high performance. Conversion of the analog input voltage into a decimal multi-digit number occurs in just two clock cycles of the digital circuit elements. The main disadvantage of such ADCs is the large number of analog comparators and flip-flops in the circuit, equal to 2 n - 1, which makes multi-bit parallel ADCs prohibitively expensive.

Significantly lower hardware costs are required in a serial ADC. In Fig. Figure 4.15 shows a tracking ADC circuit that belongs to the group of sequential circuits. The diagram uses previously unmentioned symbols: GTI- clock pulse generator, SR- reverse counter, TO- comparator, R- output register. Designations of logical elements AND,OR NO generally accepted.

Comparison U in And U e performed on a combined analog comparator with two outputs: “more than” (>) and “less than” (<). ЕслиU in - U e >ΔU 0/ 2, then a single signal appears at the output >, and the element And 1 conducts clock pulses to the summing input (+1) of the up/down counter SR. The output number is growing SR, and increases accordingly U uh, generated DAC. If U in - U e < ΔU 0 /2 , then a single signal appears at the output< , при этом импульсы от генератора тактовых импульсов через элемент AND 2 pass to the subtraction input (-1) of the counter SR And U e decreases. When the condition | U in - U e | = ΔU 0 /2 on both outputs TO zero signals and elements are highlighted And 1 And AND 2 are locked for clock pulses. The counter stops counting, and the number remaining unchanged at its output appears at the register output R. Permission to write a number to a register is given by a single element signal OR-NOT, included on two outputs TO. Considering this scheme in relation to U in And U uh, it can be established that the ADC is a control system closed along the output coordinate with a controller TO relay action. The system monitors the change in input voltage with a steady-state accuracy of ± U 0 /2 and outputs a number corresponding to the digital output U in. A tracking ADC can quickly convert only a fairly slow change in input voltage.

The main disadvantage of the considered ADC is its poor performance. In the most unfavorable case, when the maximum voltage at the input is abruptly set, to produce the corresponding output value in a digital code it will be necessary 2 n - 1 beats Some DAC and ADC circuits and their operation are discussed in /1/.

Self-test questions

1. Why are matching elements used in automation systems?

2. What transformation is carried out by a phase detector?

3. In what modes can the phase detector operate?

4. What are the input coordinates of the phase detector?

5. What is the output coordinate of a phase detector?

6. What is the amplitude operating mode of a phase detector?

7. What is the phase mode of operation of a phase detector?

8. What can phase detectors be used for in automation systems?

9. Give the formula for the control characteristics of a phase detector operating in amplitude mode.

10. What conversion is carried out by a digital-to-analog converter?

11. What are the input and output coordinates of a digital-to-analog converter?

12. What are the main parts of a digital-to-analog converter circuit?

13. Give formulas for calculating the control characteristics of a digital-to-analog converter and its average transmission coefficient.

14. What type of control characteristic does a digital-to-analog converter have?

15. What conversion is carried out by an analog-to-digital converter?

16. What are the input and output coordinates of an analog-to-digital converter?

17. Give formulas for calculating the control characteristics of an analog-to-digital converter and its average transmission coefficient.

18. What types of analog-to-digital converters are there?

19. What are the main advantages and disadvantages of parallel analog-to-digital converters?

20. What are the main advantages and disadvantages of serial analog-to-digital converters?

21. Why is a digital-to-analog converter used in an analog-to-digital converter tracking circuit?

22. What is the maximum steady-state absolute conversion error of a tracking analog-to-digital converter?

SENSORS

Self-test questions

1. What are the input and output coordinates of the rotation angle sensor?

2. What are the input and output coordinates of the misalignment angle sensor?

3. In what systems can angle sensors and error sensors be used?

4. How many windings and where does the three-phase contact synchro have it?

5. What are the input and output coordinates of the selsyn?

6. In what modes can the selsyn operate?

7. What is the amplitude mode of operation of a synchronizer?

8. What is the phase mode of operation of a selsyn?

9. Give a formula for calculating the control characteristics of a synchronizer in amplitude operating mode.

10. Give a formula for calculating the control characteristics of a synchronizer in the phase mode of operation.

11. What factors determine the static errors of a synchronizer that distort its control characteristics?

12. What causes the speed error of the rotary angle sensor based on the selsyn?

13. In what mode do the selsyn sensor and selsyn receiver operate in the mismatch angle sensor circuit if the amplitude value of the EMF of the rotor of the selsyn receiver and the phase of this EMF are used as its output coordinates?

14. Give a formula for calculating the control characteristics of a mismatch sensor based on two synchronizers operating in transformer mode.

15. What are the main disadvantages of rotary angle sensors based on selsyn?

16. For what purpose are reduction measuring gears used at the input of rotation angle sensors?

17. For what purpose are step-up measuring gears used at the input of rotation angle sensors?

18. How does the angle measurement error change when using reduction measuring gears?

19. When is it appropriate to use discrete angle sensors?

20. What are the main elements present in the design of a digital rotation angle sensor based on a code disk?

21. Why does the control characteristic of a digital rotation angle sensor based on a code disk have a stepwise character?

22. Give a formula for calculating the discrete interval of a digital rotation angle sensor based on a code disk.

23. Give a formula for calculating the absolute error of a digital rotation angle sensor based on a code disk.

24. By what design measures can the bit capacity of a digital rotation angle sensor based on a code disk be increased?

Angular speed sensors

DC tachogenerator is a direct current electric machine with independent excitation or permanent magnets (Fig. 5.6). Input coordinate TG - angular velocity w, output - voltage U out, allocated to the load resistance.

E tg = kФw = I(R tg + R n),

Transfer coefficient TG, V/rad; k = pN/ (2p a)- constructive constant; F- magnetic excitation flux; R tg- resistance of the armature winding and brush contact.

The transfer coefficient of the TG, strictly speaking, does not remain constant when the speed changes due to the nonlinearity of the brush contact resistance and the armature reaction. Therefore, a certain nonlinearity is observed in the control characteristic in low and high speed zones (Fig. 5.6, b). Nonlinearity in the low-speed zone is reduced by using metallized brushes with a low voltage drop. The nonlinearity of the characteristic due to the armature reaction is reduced by limiting the speed from above and increasing the load resistance. When carrying out these activities, the control characteristics of the TG can be considered almost straightforward.

Operational amplifier: switching circuits, operating principle. Non-inverting operational amplifier amplifier circuit

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