RU2403607C2 - Relay regulator - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: relay regulator has first and second comparators, first and second integrators, first and second relay elements, an adder and an on-off signal generator. The law of generating the output signal is defined by amplifier parametres - amplification coefficient and a limiting value, as well as the level of the output signal of the first relay element and limitating level of the second integrator.

EFFECT: relay regulator increases dynamic accuracy of angular deviation in the transient process and dynamic accuracy in angular velocity in the steady state during disturbing moments, which improves dynamic characteristics of the relay regulator.

6 dwg

Description

The invention relates to automation and can be used in control systems for various inertial objects, for example, turntables, industrial robots, aircraft.

Mostly the inventive device is intended for use in the spacecraft (SC) control system in the mode of its manual control in the process of convergence and docking with another device.

In the process of rendezvous, automatic maintenance of a given angular position of the spacecraft relative to the direction of approach with another spacecraft also having a stabilized angular position is preliminarily ensured. Then, in the manual control mode, the longitudinal movement of the first spacecraft to a predetermined reference point of the second spacecraft is maintained while maintaining minimum linear speeds and deviations relative to the approach direction. The correctness of the approach control is ensured by maintaining the position of the landmark in a given (central) region of the optical means through which the landmark is observed. A “departure” of a reference point from a given area can be caused either by the longitudinal displacement of the spacecraft relative to the line of approach, or by its angular displacements. In order to “untie” the longitudinal displacements from the angular motions of the spacecraft, it is necessary to ensure extremely low speeds of the latter. In this case, the angular movements will not affect the control of the linear movements of the spacecraft.

The inventive device belongs to the class of devices providing low speeds of adjustable parameters in the process of maintaining given errors of positional deviations, in particular to ensure the minimum possible angular velocities in the process of maintaining a given angular deviation of a spacecraft.

Known relay controller [1], comprising an adder, a relay element covered by integrating negative feedback, and a controlled pulse shaper.

The disadvantage of this device is that it has low noise immunity and a limited operating range determined by the linear (information) zone of the position deviation sensor.

A relay controller [2] is also known, which contains a serially connected positional deviation signal bus, a comparator, a limited amplifier, an adder and an integrator covered by negative feedback from the integrator output to the inverting input of the comparator device, as well as a relay element and a relay signal shaper connected in series with a delay on shutdown.

The disadvantage of this relay controller is that it cannot provide small (set) dynamic errors of the control system, which includes the specified controller, if external disturbances act on the control object.

The closest in functional construction to the claimed device is a relay controller [3].

The prototype device [3] contains a serially connected positional deviation signal bus, a comparator, a limited amplifier, an adder, an integrator covered by negative feedback from the integrator output to the inverting input of the first comparator, a second comparator and a limited integrator, the output of which is connected with the inverting input of the second comparison device. The prototype device also contains a series-connected three-position relay element and a shaper of the relay signal with a delay on off, the input of which is connected to the output of the three-position relay element and the second inverting input of the adder, the third non-inverting input of which is connected to the signal signal of the rate of change of the positional deviation.

The specified device provides a given accuracy of maintenance in steady-state conditions, including under the action of external disturbances.

However, the use of the known device in the control system does not allow to achieve its high dynamic accuracy: to eliminate or reduce to predetermined limits the overshoot in terms of the rate of change in positional deviation in the case of damping its large initial speeds and when practicing emerging external disturbances on the control object.

The objective of the invention is to increase dynamic accuracy during control under conditions of action of external disturbances on the control object and when practicing large initial velocities of positional deviation.

This problem is solved in that the relay controller containing the positional deviation signal bus connected in series, the first comparator device, limiter amplifier, adder, integrator, covered by negative feedback from the integrator output to the inverting input of the first comparator device, the second comparator device and integrator with a restriction, the output of which is connected to the inverting input of the second comparator device, as well as a three-position relay element connected in series and a shaper of the relay signal with a delay for switching off, the input of which is connected to the output of the three-position relay element and the second inverting input of the adder, the third non-inverting input of which is connected to the signal bus of the rate of change of positional deviation, a second adder is added, connected in series between the output of the second comparison device and the input a three-position relay element, a second limiter amplifier and a multiplication unit, the output of which is connected to the second inverting by the input of the first adder, the first input of the multiplication unit is connected to the output of the three-position relay element, the second input of the multiplication unit is connected to the output of the second comparison device and the input of the limiter amplifier, the output of which is connected to the input of the integrator with restriction and the second input of the second adder, while the zone value the insensitivity of the three-position relay element is chosen less than or equal to the limit level of the amplifier-limiter.

Figure 1 shows a block diagram of a relay controller. In this diagram:

1, 7 - a comparative device (the first and second - respectively),

2, 8 - amplifier-limiter (the first and second - respectively),

3, 10 - adder (first and second - respectively),

4 - integrator

5 - three-position relay element,

6 - shaper relay signal with a delay on shutdown (according to the description - FRSV 6),

9 - integrator with restriction,

11 - multiplier,

12 - bus signal positional deviation (hereinafter - SHSPO 10),

13 - bus signal of the rate of change of positional deviation (hereinafter - SHSSIPO 11),

14 - output bus relay controller

15 - control object (not included in the controller; it is shown for completeness of the description of the technical result from the use of the claimed device).

Figure 2 shows a phase portrait of a system with a relay controller in the control loop.

Figure 2 shows:

X, Y - phase coordinates of the control system (in accordance with figure 1),

L ₀ , L ₀ ^- , L ₁ , L ₁ ^- - switching lines,

L ₂ , L ₃ , L ₂ ^- , L ₃ ^- - off lines,

a - phase trajectories,

s is the boundary of the region of the sliding mode (for X> 0).

Figure 3-6 shows the phase portraits of the spacecraft control system when using the claimed device (figure 3 and 5) and the known device (figure 4 and 6). These phase portraits are obtained as a result of mathematical modeling and are intended to compare the characteristics of the claimed and known devices.

In the relay controller ShSPO 12, the first comparator 1, the first amplifier-limiter 2, the first adder 3, the integrator 4, the second comparator 7, adder 10, the three-position relay element 5, FRSV 6 are connected in series. The output of the integrator 4 is connected to the inverting input of the first comparison device 1. The output of the three-position relay element 5 is connected to the second inverting input of the first adder 3, the third non-inverting input of which is connected to the SHCCIPO 13, and to the input of the multiplier 11. The output of the second comparative device 7 is connected through the second amplifier -limiter 8 with an integrator input with a restriction of 9, connected by its output to the inverting input of the second comparison device 7. The output of the second amplifier-limiter 8 is connected to the second input of the second adder 10. The output of the FRSZV 6 is the source of the control action My (see Fig. 1) on the control object 15. ShSPO 12 and ShSSIPO 13 are the input signals of the relay controller characterizing the output phase coordinates of the control object 15.

Consider the operation of the relay controller on the example of controlling the orientation of the spacecraft (control object 15). Let the signal X of the angular (positional) deviation of the spacecraft and the signal Y (SHSSIPO 13) of the rate of change of the angular deviation (angular velocity) be received at the inputs (SHSPO 12) of the relay controller. The task of the relay controller is to form the signal My (the output signal of the FRPCS 6 of the relay signal with delay) in order to reduce the signals X and Y to the steady state region A⇒X∈ (-h, + h), Y∈ (-Y ₀ , + Y ₀ ), where the values of ± h determine the dead zone of the relay controller, the values of ± Y ₀ determine the permissible values of the angular velocity in the steady state (dead zone of the relay controller according to the angular velocity) - the mentioned parameters are shown in figure 2.

The relay controller in the control system is described as follows

where My, Mв are controlling and disturbing moments, respectively.

Further in the text: U _i - state variables of the relay controller (output signals of functional blocks with corresponding positional designations).

where U _i ^m are fixed (in the role of parameters) values of the variables U _i (m is any index). Hereinafter: K _i - transmission coefficients of variables U _i .

In particular, U ₂ and U ₂ ^{+ -} - value amplifier-limiter level 2. These values determine the position shutdowns lines L ₃ and L ₃ ^- the phase portrait (Figure 2). The value of K ₂ determines the slope of the shutdown lines L ₂ and L ₂ ^- .

) - первая производная от сигнала U₄.Expression (6) connects the signals at the input and output of the integrator 4 (

) is the first derivative of the signal U ₄ .

Hereinafter, h ₁ is the deadband value of the three-position relay element 5, ± Y ₀ are the admissible values of the angular velocity in the steady state, τ is the delay for switching off the FPGA 6.

Expression (8) describes the static characteristic of a three-position relay element 5 as a three-position relay element without hysteresis. In practical implementation, the value of the hysteresis should be minimal, but sufficient to ensure the frequency mode of operation of the executive bodies.

where U ⁺ ₆ and U ⁺ ₅ are the positive values of the signals U ₆ and U ₅ ,

U ^- ₆ and U ^- ₅ - negative values of the signals U ₆ and U ₅ ,

Ф (τ) ⇒t ₆ = t ₅ + τ - means the conversion of the relay signal U _{5 of} duration t ₅ into the relay signal U _{6 of} duration t ₆ .

In relation to the impact on the control object 15, the signal U ₆ is the control moment My.

The laws of formation of the output signal My of the relay controller, which allow bringing the coordinates X and Y into the region of the stable state A, are determined by expressions (3-15).

Let us dwell on the characteristics of some elements of the flowchart. The integrator with restriction 9 has an output signal U ₉ limited by the value ± h ₂ , the value | h ₂ + h ₁ | = | h | corresponds to the boundary of the dead zone of the relay controller in the steady state of the control system. The operating levels ± h _{1 of the} three-position relay element 5 are selected by the absolute value significantly less than | ± h | (let h ₁ = 0.1 h). The restriction levels of the second amplifier-limiter 8 are chosen equal to ± Y ₀ (corresponds to the permissible value of the angular velocity in the steady state).

Consider the operation of a relay controller.

Let the signal X increase from zero at a speed Y> Y ₀ (plot a ₁ -a _{2 of the} path a). In this case

due to the fact that the signal U ₈ does not exceed the absolute value of Y ₀ . There is an increase in the signals U ₂ , U ₄ , U ₇ . When the signal U ₇ reaches the value of h _{1, the} three-position relay element 5 (point a _{2 of the} trajectory) is turned on, forming the output signal U ₅ , which is fed to the second inverting input of the first adder 3, the input of the multiplier 11 and the input of the FPGA 6, the output signal My of which is the output signal of the regulator and is used to turn on the executive motors. FRSV 6 is a relay element with a delay on shutdown: the operation of the FRSV 6 occurs simultaneously with the tripping of the three-position relay element 5, and the shutdown - in time τ after the first relay element 5 is turned off (see 11-13).

If the position of the image point (signals X and Y) is above the line S (the boundary of the "sliding mode" [4]) - sections a ₂ -s ₁ , a ₆ -s ₂ , then the three-position relay element 5 is switched on continuously. When falling into the sliding mode region (sections s ₁ -a ₃ onwards, s ₂ -a ₇ onwards) in the circuit: the first comparison device 1, the first amplifier-limiter 2, the first adder 3, the integrator 4, the second comparison device 7, three-position relay element 5, a sliding mode occurs, which is characterized by the switching of the three-position relay element 5 with a frequency f _p determined by the rate of change of the signal X (angular velocity Y). If f _p > 1 / τ, then the output signal My of the controller is continuous (sections s ₁ -a ₃ , s ₂ -a ₇ ). If f _p <1 / τ, then the output signal My of the controller is relay-pulse, frequency f _p and duration τ (for example, section a ₇ -a ₈ ). The inclusion of the FRSZV 6 ensures that the coordinates X, Y are brought into the region of the stable state A (plot a ₈ -a ₉ -a ₄ ).

For signal X, the position of the turn-on line L ₀ at the first moment corresponds to the boundary h _{1 of} the deadband of the three-position relay element 5. After its inclusion, due to the action of negative feedback signals (signals U ₅ and U ₁₁ ), the “turn” of the turn-on line (as well as the turn-off lines) ) in the direction of p ⁺ . The position of the shifted on and off lines is indicated by a dotted line. In particular, for example, the output from the continuous on mode occurs on a biased off line at point a ₇ . When you turn off the three-position relay element 5 with decreasing signal X (for example, section a ₈ -a ₉ ), the switching lines shift in the p ⁺ direction. The offset occurs at a constant speed if the signal U _{2 is} limited by the values of U ₂ ⁺ , U ₂ ^- (4) and with a decreasing (in absolute value) speed if the signal U ₂ is located on a linear section of the first amplifier-limiter 2.

By choosing the slope and limiting the output characteristic of the first amplifier-limiter 2, the required parameters of the switching lines of the relay controller are achieved, in particular, the gain of the amplifier-limiter 2 determines the slope of the lines L ₂ and L ₂ ^- , its level of limitation determines the position of the lines L ₃ and L ₃ ^- .

Next, let the signal X increase from zero at a speed Y <Y ₀ (plot a _{4-a 5 of the} path a). In this case, the output signal U _{4 of the} integrator 4 is equal to the signal X, which is provided by the structure of the circuit formed by the first comparison device 1, the first amplifier-limiter 2, the first adder 3 and the integrator 4, and the output signal U _{7 of the} second comparison device 7 is less than h ₁ , since the output signal U _{9 of the} integrator is monitored with a restriction of 9 for the output signal U _{4 of the} integrator 4. In this case, the three-position relay element 5 is turned off, which corresponds to the steady state mode, for which X, Y∈A coordinates (A is the “steady state” mode region: low speeds, deviations within a given deadband).

Let, for example, now the signal X increases from zero with a constantly increasing speed (section a ₁₀ -a _{11 of the} path a) and at some moment the condition Y> Y ₀ (point a ₁₁ ) is fulfilled - this process occurs when an external constant is applied to the control object indignation. Starting from the indicated moment, the signal U ₈ rapidly increases to the level Y ₀ ; in accordance with (16), the signal U ₄ starts to “outrun” the signal U ₉ by the value of h ₁ . The simultaneous action of signals U ₇ and U ₈ leads to the operation of the three-position relay element 5 (point b). Next: switching on the FRSZV 6 → starting the “quenching” of the speed → turning off the three-position relay element 5 → turning off the FRSZV 6 → then, due to the increase in speed, the three-position relay element 5 is triggered and the process is repeated. Thus, a speed stabilization mode is provided, the value of which is close to the value of Y ₀ .

The value of h _{1 is} chosen close to the value of Y ₀ , therefore, the three-position relay element 5 is forcedly turned on, and then its inclusion is maintained due to the action of the signal U ₄ .

Calculations and mathematical modeling show that the gain of the first amplifier-limiter 2 should be selected in the range from 0.3 to 0.8, and the gain of the second amplifier-limiter 8 should be selected from 5 to 15.

An analytical assessment of the effectiveness of the proposed relay controller is extremely cumbersome. It is better to show the effectiveness by comparing phase portraits obtained by mathematical modeling of the proposed and well-known relay controllers. The following processes were simulated with a gain of the first limiter amplifier 2 equal to 0.67 and a gain of the second limiter amplifier 8 equal to 10.

Figures 3 and 4 show the processes of changing the control error X and the speed of the control error Y when parrying an external disturbance in the conditions of the initial values X = 0, Y = 0 when using the proposed (Fig. 3) and known [3] (Fig. 4) devices.

A comparative analysis of the processes shows that when using the known device, there is overshoot to the level of 0.145 at a given steady-state value of 0.05 (a predetermined steady-state speed value corresponds to the limiting levels of amplifier-limiter 8), i.e. overshoot ΔY almost reaches 200%.

Figures 5 and 6 show the processes of changing the control error X and the speed of the control error Y when working out the initial speed Y = 5 under the conditions of the initial value X = 0, using the proposed (Fig. 5) and known [3] (Fig. 6) devices.

A comparative analysis of the processes shows that, when using the known device, the control system has overshoot ΔY to approximately minus 3.0 for a given rate of reduction to the steady-state region minus 1.0 (the given steady-state value of the reduction rate corresponds to the limiting levels of amplifier-limiter 2), i.e. overshoot also almost reaches 200%. At an initial speed of Y = 4, the overshoot reaches minus 1.8.

This positive effect is achieved by the combined action of an additional signal (U ₁₁ ) of negative feedback coming from the output of the multiplier 11 and an additional component (signal U ₈ ) in the signal U ₁₀ at the input of the three-position relay element 5: the signal U ₈ reduces the deadband for the signal U ₇ , and the action of the signal U ₁₁ increases the damping properties of the negative feedback loop of the relay controller.

The proposed set of features in the solutions considered by the authors was not found to solve the problem and does not follow explicitly from the prior art, which allows us to conclude that the technical solution meets the criteria of "novelty" and "inventive step". As elements for implementing the device, standard elements can be used: amplifiers, integrators, relay elements, comparing devices, adders.

Literature

1. SU. Copyright certificate 1137472, cl. G05B 11/14, 1985.

2. RU. Patent 2115150, CL G05B 11/14, 13/02, 11/01, 1998.

3. RU. Patent 2223528, cl. G05B 11/14, 2004 (prototype).

4. Utkin V.I. Sliding modes and their application in systems with variable structure. M. Science, 1981, pp. 233-240.

Claims (1)

A relay controller containing a serially connected positional deviation signal bus, a first comparator, a first limiter amplifier, a first adder, an integrator, which are negatively coupled from the integrator output to the inverting input of the first comparator device, a second comparator and a limiting integrator whose output is connected with the inverting input of the second comparison device, as well as the three-position relay element and the driver connected in series a relay signal with a delayed shutdown, the input of which is connected to the output of the three-position relay element and the second inverting input of the adder, the third non-inverting input of which is connected to the bus signal of the rate of change of positional deviation, characterized in that it additionally introduced a second adder connected in series between the output of the second the comparator device and the input of the three-position relay element, the second limiter amplifier and the multiplication unit, the output of which is connected to the second the inverting input of the first adder, the first input of the multiplication unit is connected to the output of the three-position relay element, the second input of the multiplication unit is connected to the output of the second comparison device and the input of the first amplifier-limiter, the output of which is connected to the input of the integrator with restriction and the second input of the second adder, the value dead zones of a three-position relay element are selected less than or equal to the level of limitation of the second amplifier-limiter.

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