JPS6395502A - Discrete optimum servo system - Google Patents

Abstract

PURPOSE:To avoid an overshoot trouble by obtaining a manipulated variable with addition of the upper load value corresponding to the state value of the present time pint as well as the deviation between the controlled variable and the target value of the present time point to the holding contents of the manipulated variable related to the preceding output against a controlled system. CONSTITUTION:When a manipulated variable (u) is given to a controlled system 9, the controlled system 9 responds to the variable (u) and at the same time the controlled variable (y) and the state value (x) of the present time point are fed back from the system 9. The variable (u) given to the system 9 is held by a sample hold circuit 19 each time. These held contents are given to an arithmetic means 17 as the manipulated variable of the preceding step when the manipulated variable of the next step is decided. The means 17 adds the deviation epsilon between the controlled variable (y) and the target value (r) of the present time point and the upper load value corresponding to the value (x) to the manipulated variable (u) of the receding time. The result of this addition is compared with the limit variable (u) by a limiter circuit 18. Then the actual variable (u) to be given to the system 9 is decided based on the result of said comparison. In such a way, an overshoot trouble is avoided.

Description

[Detailed Description of the Invention] <Industrial Application Field> This invention determines the manipulated variable (control input) so as to minimize the evaluation function for a discrete time system, and changes the state of a controlled object from an initial state to a final state. In relation to a discrete optimal servo system for transitioning to a state, the present invention provides a new control method in particular when there is a limit to the magnitude of the manipulated variable.

<Conventional technology> Now m input,! Consider an integral optimal regulator for a discrete time system expressed by the following equation 00 with an output and n states.

In the above formula, X is the state vector, U is the input vector, and y
is the output vector, and A, B.

C is a constant matrix.

First, let the target value vector of the control output be r, and then we obtain an expanded system as follows. Next, for this expanded system, the next 0
Consider the evaluation function expressed by the formula.

+v'' (k)Rv (k)) -...-■ Here, Q and R are positive definite symmetric matrices.

In this case, since (C, A) is observable, the expanded system is also observable, but even if (A, B) is reachable, the expanded system is not necessarily reachable. The necessary and sufficient conditions for an extended system to be reachable are:
The following equation 0 holds true.

Thus, under the above equation 0, the optimal input increment VO(k) that minimizes the evaluation function J[V] is expressed in the form of the following [phase] equation.

However, K is the state feedback gain + KI is the integral gain.

Therefore, the optimal input (operated amount) corresponding to this vo (k)
uo(k) is expressed by the following 02 using the equation (2), and the block diagram of this servo system is shown in FIG.゛+ [uo (0) Kx (Q)
, , , 0 In Equation 0, the first term on the right side represents the state feedback amount, and the second term represents the cumulative value of target value deviation,
The following terms indicate initial values.

Furthermore, in the above equation, ε (i) in the second term is set to ε (k)=O for k<Q.

In the conventional discrete optimal servo system, the manipulated variable u0 (k) of the controlled object is determined by the above equation 0, but there are cases where restrictions are placed on the control input (manipulated amount) depending on the ability of the controlled object, etc. .

FIG. 7 shows an algorithm of a conventional control method when there is this kind of restriction. Step 1 in the same figure (rsTI in the figure
After initializing the number of steps k in step 2 (denoted by J), in the next step 2, the manipulated variable uo(k) is changed to the cumulative value of the state quantity feedback quantity Kx (k) and the target value deviation, Σε N
) and the initial value s0 [uo (0)-Kx (0)] (see ■2). Next, in step 3, this manipulated variable uo(k)
is compared with the limit values u,,l, and the manipulated variable uO(k
) exceeds the limit value u1 (step 3 is “YES”).
”), the process proceeds to step 4, where the limit value U is output as the actual control input. On the other hand, the manipulated variable uo(k) is the limit value u6
In the following cases (“No” in step 3), the manipulated variable uO(k) is output as is in step 5. Then, in step 6, the number of steps k is updated, and the process returns to step 2, where similar calculations and processing are repeatedly executed.

<Problems to be Solved by the Invention> However, in the case of the above control method, the second term on the right side of the above equation 0, that is, the cumulative value of the target value deviation, has a value of 1Σε (
Since i) becomes excessive, a large overshoot may occur in the output (controlled amount) to be controlled sl.

FIG. 8(a) shows a response waveform of the control output (control 111u) to the control input (operated amount) shown in FIG. 8(b). In the figure, u indicates the limit value of the control input, and r indicates the target value of the control output, and it can be seen that a large overshoot (indicated by S in the figure) has occurred in the control output. .

Such overshoot causes problems such as lengthening the settling time of the control system and leading to destruction of plant equipment.

To deal with this problem, methods have been proposed such as calculating parameters with low gains so that the manipulated variable does not exceed the limit value (for example, "Numerical solution method for linear quadratic optimal control problem with state constraints"). Since this method is a passive method of keeping the gain of the control parameter low, it has the drawbacks of poor controllability against disturbances and poor coordination.

This invention is intended to solve the above problem,
The purpose of the present invention is to provide a discrete optimal servo system that can suppress overshoot to a small level even when the control parameter has a high gain.

<Means for Solving the Problems> In order to achieve the above object, the present invention employs a discrete optimization method in which the state of the controlled object is shifted by determining the manipulated variable so as to minimize the evaluation function for the discrete time system. In a servo system, there is a holding means for holding the manipulated variable related to the previous output for the controlled object, and a deviation between the current target value and the controlled variable with respect to the manipulated variable held by the holding means, and the current state Mffi. The present invention is equipped with a calculation means for adding an additional product amount according to the amount of product, and a regulation means for regulating the calculation result of the calculation means by a limit value of the manipulated variable and applying it to the controlled object.

<Operation> When a manipulated variable is given to a controlled object, the controlled object responds to this, and the controlled variable and state B amount at the present moment are fed back from the controlled object. The manipulated variable applied to the control object is held in the holding means each time, and when determining the manipulated variable of the next step, the contents of this retention are given to the calculation means as the manipulated variable of the previous step. This calculation means adds an additional product amount corresponding to the deviation between the current control amount and the target value and the current state C and amount to the previous operation amount, and provides the result of the addition to the regulation means. This addition result is compared with the limit value of the manipulated variable by the regulating means,
The actual amount of operation to be applied to the controlled object is determined according to the comparison result.

In this method, unlike the conventional example, the accumulated value of the target value deviation which becomes excessively large is not used as a determining factor for the manipulated variable, so that a large overshoot in the output (controlled variable) of the controlled object is prevented from occurring.

<Embodiment> FIG. 1 shows an example of the configuration of an optimal servo system according to an embodiment of the present invention, and FIG. 2 shows an example of application to which this servo system is applied.

The application example of FIG. 2 is a temperature control system for an electric furnace, which includes an electric furnace I, a heater 2 for heating the electric furnace, and information a such as the temperature inside the furnace from the electric furnace I. The controller 3 also includes a controller 3 for obtaining operation amount information from the heater 2, executing predetermined calculations, and giving necessary commands C to the heater 2. As shown in FIG. 3, this controller 3 includes a CPU 4. It is composed of a microcomputer consisting of ROM5, RAM6, etc., and the CPU4 is R
It decodes and executes the program of OM5, reads and writes data to RAM6, and executes calculations and processes necessary for temperature control of the electric furnace. Note that FIG. 3 shows a general hardware configuration of this type of control system, and the sensor 7 in the figure is the second
In the case of the application example shown in the figure, the actuator 8 corresponds to a temperature sensor such as a thermocouple installed in the electric furnace 1, and the actuator 8
The controlled object 9 corresponds to the electric furnace 1, respectively.

The above-mentioned controlled object 9 corresponds to the part shown by the broken line in the block diagram shown in FIG. 12, and also the shape LEIx (
k) is provided to the difference circuit 14 via the second feedback loop 11.

The calculation unit 12 calculates the target value r of the manipulated variable and the control ff.
The deviation ε (k) from
(k) is given an integral gain of 1 and output to the calculation section 16.

On the other hand, in the differential circuit 14, the current state If? x(k)
The difference ξ (k
) is calculated (corresponding to the calculation of the above equation 0), and in the next block 15, the state feed parameter is calculated.

A gain K is given and output to the arithmetic unit 16.

This calculation unit 16 executes calculations based on the [phase] formula, that is, addition calculations of the outputs from each block 13.
(k) is calculated, and the calculation result is given to the next calculation unit 17.

This calculation unit 17 calculates the operation amount u (k-1) given to the controlled object 9 in the previous step and the increment Vo Nc)
By adding these, the manipulated variable uo (k) is determined and output to the limiter circuit 18. This limiter circuit 18
compares the manipulated variable uO(k) with the manipulated variable limit value u1 to obtain the manipulated variable iu. (k) exceeds the limit value u0, the limit value u1 is used as the actual operation iu (k), and the controlled object 9
and the operation ff1uo (k) is the limit value um
In the following cases, the operation ff1uo (k) is output to the controlled object 9 as the actual operation amount u (k).

This operation ff1u (k) is temporarily held in the sample hold circuit 19 every time it is output from the limiter circuit 18, and this held content is used by the arithmetic unit 17 to calculate the operation amount uo ( k) is given to the arithmetic unit 17 from the sample hold circuit 19 as an operation 1u(k-1) related to the previous output.

FIG. 4 shows an algorithm of the control method using the above-mentioned discrete type optimal servo system. First, in step 11 of the figure, the number of steps k is initialized, and then in step E 2, an increment vo (k
) is calculated. Then, in step 13, the manipulated variable U
. (k) is the previous manipulated variable u(k-1) and the increment V. (
k), and then in the next step 14, this operation ff1uO(k) is compared with the limit value U. As a result, when the operation amount uo (k) is less than or equal to the limit value U, step 14 is "No", and the operation ff1uo (k) is output as the actual operation ff1u (k) (step 16). . On the other hand, the amount of operation uo
When (k) exceeds the limit value U, step 14 returns "Y".
ES", and in this case, the limit value u1 is the operation lu (
k) (step 15.16
).

Then, in step 17, the number of steps is updated, and the process returns to step 12, where similar calculations and processing are repeatedly executed.

Figure 5 shows the simulation results of the discrete optimal servo system according to the present invention, and Figure 5(a)
shows the response waveform of the control my (k) to the operation i7u (k) shown in FIG. 5(b). According to the figure, it can be seen that the overshoot is suppressed to a small level compared to the conventional example shown in FIG. 8.

<Effects of the Invention> As described above, in a discrete optimal servo system when there is a limit on the magnitude of the manipulated variable, the present invention stores the manipulated variable related to the previous output for the controlled object, and stores the manipulated variable related to the previous output for the controlled object. On the other hand, since we decided to obtain the manipulated variable by adding the additional product amount according to the deviation between the current target value and the controlled variable and the current state variable, the output (control) of the controlled object is obtained as in the conventional example.
+B N ) can be prevented from causing a large overshoot. Therefore, the settling time of the control system can be shortened, and destruction of plant equipment can be prevented. Furthermore, even if the control parameter has a high gain, overshoot can be suppressed to a small level, so that the controllability against disturbances is good, the coordination is also good, and other remarkable effects are achieved that achieve the purpose of the invention.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the configuration of a discrete optimal servo system according to an embodiment of the present invention, FIG. 2 is an explanatory diagram showing a schematic configuration of an application example of the invention, and FIG. 3 is an application of FIG. A block diagram showing an example of the hardware configuration, FIG. 4 is a flowchart showing an algorithm of the control method according to the present invention, and FIG. 5 shows changes in the manipulated variable and the controlled variable in the discrete optimal servo system of the present invention. Explanatory diagram, No. 6
FIG. 7 is a block diagram showing the configuration of a conventional example, FIG. 7 is a flowchart showing an algorithm of the conventional control system, and FIG. 8 is an explanatory diagram showing changes in the manipulated variable and the controlled amount in the conventional example. 9... Controlled object 12.16.17... Arithmetic unit 14... Differential circuit 18... Limiter circuit 19... Sample hold circuit patent Applicant Tateishi Electric Co., Ltd. Agent Patent Attorney Mitsuru Suzuki Yama-■ ”+ztw kon J-m n ilk l”R4
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Claims (3)

[Claims] (1) In a discrete optimal servo system that changes the state of a controlled object by determining a manipulated variable to minimize the evaluation function for a discrete time system, the manipulated variable related to the previous output for the controlled target is retained. a calculation means for adding an additional product amount according to the deviation between the current target value and the control amount and the current state quantity to the manipulated variable held by the holding means; A discrete optimal servo system is provided with a regulating means for regulating the calculation result by a limited value of the manipulated variable and applying it to a controlled object. (2) The discrete optimal servo system according to claim 1, wherein the holding means is a sample and hold circuit. (3) The discrete optimal servo system according to claim 1, wherein the regulating means is a limiter circuit.