JPH04302302A - Two degree of free controller - Google Patents

Abstract

PURPOSE:To quickly decide a control constant to perform control with high accuracy compared with the case that a feedforward control constant is found as applying a trial and error. CONSTITUTION:This controller is provided with a feedback control arithmetic means 2 and a feedforward control arithmetic means 4 which control a controlled system 1. The feedback control constant of the feedback control arithmetic means 2 can be found by a feedback control constant arithmetic means 3. The feedforward control constant of the feedforward control arithmetic means 4 can be found by a feedforward control constant arithmetic means 5. An evaluation function decision means 6 designates an appropriate transfer function relating to the feedforward control arithmetic means 4, and finds an evaluation function for a transfer function. The feedforward control constant arithmetic means 5 finds the feedforward control constant so as to set the evaluation function at the minimum value or a value less than an allowable value.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a two-degree-of-freedom control device having two functions: a feedback control function and a feedforward control function.

0002

2. Description of the Related Art The basic method of constructing a two-degree-of-freedom control device has been known for some time. For example, (1) Araki: 2 Degrees of Freedom Control System-I, System and Control Vo
l. 29, No. 10, pp. 649-656, (19
85) (2) Hara, Sugie: 2 Degrees of Freedom Control System-II, System and Control Vol. 30, No. 8, pp. 45
7-466, (1986), etc. The basic structure of a two-degree-of-freedom control device is a feedback control calculation means that calculates the amount of operation to the controlled object based on the output signal of the controlled object, and a feedforward system that calculates the operational input to the controlled object based on the target input signal. and control calculation means. The feedback control calculation means is designed to improve closed-loop characteristics, such as the sensitivity characteristics and complementary sensitivity characteristics of a closed-loop system, while the feedforward control calculation means is designed to improve closed-loop characteristics such as the sensitivity characteristics and complementary sensitivity characteristics of a closed-loop system, while the feedforward control calculation means is designed to improve the closed-loop characteristics, such as the sensitivity characteristics and complementary sensitivity characteristics of a closed-loop system, while the feedforward control calculation means is designed to improve the closed-loop characteristics such as the sensitivity characteristics and complementary sensitivity characteristics of a closed-loop system, while the feedforward control calculation means is designed to improve the closed-loop characteristics such as the sensitivity characteristics and complementary sensitivity characteristics of a closed-loop system. It is designed to improve its response characteristics. In the two-degree-of-freedom control device, the feedback control calculation means and the feedforward control calculation means can be designed separately, so the closed loop characteristics and the target value tracking characteristics can be independently improved.

When configuring the feedback control calculation means, various configuration methods have been used in the past, such as a PID control device, a control device by combining an LQ optimum regulator and a Kalman filter, and a control device by the H∞ control system design method.

On the other hand, regarding the design method of the feedforward control calculation means, the structure of the controller is determined in advance like a two-degree-of-freedom PID control device, and the control constants are determined by trial and error while looking at the response waveform. The other method is the model matching method, in which a reference model indicating a desired target value response is prepared and a feedforward control device is designed so that the transfer function of the control system matches the transfer function of the reference model.

[0005]

[Problem to be solved by the invention] However, when using a trial-and-error method, it is easy to adjust the control constants if only the target value response characteristics are improved, but there are multiple design goals to consider at the same time. In some cases, adjusting the control constants requires a lot of experience and time. Furthermore, since the structure of the control device is predetermined, depending on the object to be controlled, there is a possibility that a control effect that is far from the limit of control performance can be obtained. Furthermore, if the controlled object is a multi-input/output system, the number of control constants to be adjusted increases, and there is also the effect of mutual interference between the controlled object inputs and outputs, so in reality, the control system is designed by trial and error. becomes quite difficult.

Furthermore, even when the model matching method is used, it is not possible to specify any model as the reference model, and there are limits to the reference models that can be specified depending on each controlled object. Therefore, depending on the controlled object, it may not be possible to select a transfer function that exhibits an ideal response as a reference model, and a model must be selected with some compromise. On the other hand, since control performance is highly dependent on the properties of the reference model, the question of what kind of properties should be compromised in is the best reference model to choose is an extremely important issue. Furthermore, when the dimension of the system is high, when a control device is designed based on multiple control specifications, or when the controlled object is a multi-input/output system, the criteria for selecting a reference model become increasingly complex. , substantially the same effort as determining control constants by trial and error is required.

The present invention was made to solve the above-mentioned drawbacks of the conventional two-degree-of-freedom control device, and it reduces the amount of effort required even when multiple design requirements are met without impairing the control effect. To provide a two-degree-of-freedom control device that can significantly reduce the amount of time required, and can perform accurate control even when the controlled object is a multi-input/output system with the same effort as for a single input/output system. The purpose is to

[0008]

[Means for Solving the Problems] The present invention provides a feedback control calculation means for calculating a manipulated variable to be applied to a controlled object from a control output signal and a target input signal, and a feedback control calculation means for calculating a feedback control constant used in the feedback control calculation means. a control constant calculation means; a feedforward control calculation means for calculating a manipulated variable to be applied to a controlled object from a target input signal; a feedforward control constant calculation means for calculating a feedforward control constant used in the feedforward control calculation means; evaluation function determining means for specifying an appropriate transfer function related to the forward control calculating means and calculating an evaluation function for this transfer function; This is a two-degree-of-freedom control device characterized in that a feedforward control constant is determined to be below a minimum value or a permissible value.

[0009]

[Operation] In the evaluation function determining means, appropriate transfer functions related to the feedforward control calculation means are specified, and evaluation functions are determined for these transfer functions, and in addition, the feedforward control constant calculation means sets the evaluation function to the minimum or allowable value. A feedforward control constant is determined as follows, and the control object is controlled by the feedforward control calculation means based on this feedforward control constant.

0010

Embodiments Hereinafter, embodiments of the present invention will be described with reference to the drawings. 1 to 6 are diagrams showing an embodiment of a two-degree-of-freedom control device according to the present invention.

In FIG. 1, a two-degree-of-freedom control device according to the present invention controls a controlled object 1 consisting of a single input/output or multiple input/output process or mechanical system. That is, the two-degree-of-freedom control device outputs a control output signal y(t) obtained by feeding back the output of the controlled object 1, and a target value r.
Feedback control calculation means 2 that calculates the manipulated variable of the controlled object 1 based on the target value r(t), feedforward control calculation means 4 that calculates the manipulated variable of the controlled object 1 based on the target value r(t), Sum of output signal u1 (t) of control calculation means 2 and output signal u2 (t) of feedforward control calculation means 4 u(t)=u1 (t)+u
2(t) is provided.

A signal u(t) obtained by calculating the output signal u1 (t) of the feedback control calculation means 2 and the output signal u2 (t) of the feedforward control calculation means 4 by the addition means 7 controls the controlled object 1. The control object 1 is controlled by the operation signal u(t). Further, the control constant used in the feedback control calculation means 2 is determined in the feedback control constant calculation means 3, and the control constant K4 (s) used in the feedforward control calculation means 4 is determined by the evaluation function. Based on the evaluation function determined by the means 6, the feedforward control constant is calculated by the feedforward control constant calculating means 5.

Next, the operation of this embodiment having such a configuration will be explained.

The feedback control calculating means 2 calculates the output signal u1 (t), which is the manipulated variable to be applied to the controlled object 1, from the output signal y(t) of the controlled object 1 and the target value r(t). be. For example, as shown in FIG. 2, the feedback control calculation means 2 calculates the target value r(t
) and the output signal y(t) of controlled object 1
e(t)=r(t)-y(t)
(1) can be used as an input signal to the control calculation device 8, and the output signal from the control calculation device 8 can be taken as u1(t).

In the feedback control constant calculation means 3,
The calculation algorithm and control constants used in the feedback control calculation means 2 are determined. Arithmetic algorithms include the PID control method, the combination of LQ optimal regulator and observer, the H∞ optimal control method, the H2 optimal control method, and all the methods conventionally used to design linear feedback control systems. Can be used. Once a calculation algorithm is selected, control constants can be determined according to conventional control constant determination procedures. Therefore, when the feedback control calculation means 2 has a structure as shown in FIG. Operation amount u
1 (t) will be calculated.

The evaluation function determination means 6 specifies an appropriate transfer function for the feedforward control calculation means 4, and calculates an evaluation function for this transfer function. Based on this evaluation function, the feedforward control constant calculation means 5 calculates a control constant K4 (s). Evaluation functions that can be used in the evaluation function determining means 6 include the H2 norm and H∞ of the transfer function or transfer function matrix.
Although the norm of a function such as the norm can be considered, in this embodiment, evaluation using the H∞ norm is used.

The general procedure for determining the evaluation function in the evaluation function determining means 6 is as follows. First, since the evaluation function determining means 6 requires information about the control constants used in the feedback control calculating means 2, the feedback control constant calculating means 3 determines the control constants of the feedback control calculating means 2, and then the following algorithm is applied.

Step 1: The control characteristics to be improved by using the feedforward control calculation means 4 are determined by n transfer functions or transfer function matrices G1 (s), G2 (s) based on the input/output relationship representing the characteristics. ,...,Gn
(s).

Step 2: Transfer functions or transfer function matrices G1 (s), G2 specified in Step 1
For (s),...,Gn (s), determine the frequency band in which the characteristics should be considered, and weight functions (including frequency weight functions or frequency-independent weight functions) W1 (s),
Specify W2 (s),..., Wn (s).

Step 3: An evaluation function is determined using the weighting function determined in step 2. That is, the weight function W
Transfer functions G1 (s), G2 (s), ..., Gn (
s), the evaluation function is

[0021]

[Equation 2] However, ‖H(s)‖∞ is H of the transfer function matrix
It is an ∞ norm and is defined by the following equation, where λmax [A] is the maximum eigenvalue of matrix A, and A* is the conjugate transposed matrix of A. The general evaluation function determination procedure explained above will be specifically explained with reference to FIG.

Step 1: Although various characteristics can be specified as control specifications, in this embodiment, two characteristics are specified. First, in order to improve the target value tracking characteristic, as shown in FIG.
e(s)=r(s)-y(s)
Transfer function Ger up to (4)
(s) is selected as the transfer characteristic to be evaluated. In this case, the transfer function G
er(s) is expressed as a function including the control constant K4(s) of the feedforward control calculation means 4. Furthermore, in order to limit the magnitude of the manipulated variable of the controlled object 1, the transfer function Gu2r (s) from the target value r(s) to the output signal u2 (s) of the feedforward control calculation unit 4 is also used as the evaluated transfer characteristic. do. In this case, the transfer function Gu2r (
s) is also determined as a function including the control constant K4 (s) of the feedforward control calculation means 4.

Step 2: In this embodiment, Ger(s) and Gu2r are used as the evaluated transfer functions in Step 1.
(s), weighting functions W1 (s), W2 (s
). Regarding the target value follow-up characteristic, if it is desired to particularly improve the follow-up ability for a low-frequency target signal, it is possible to select W1 (s) such that the gain frequency characteristic is as shown in FIG. 3, for example. Regarding the magnitude of the operation amount, if it is desired to reduce the operation input having a high frequency component, it is sufficient to set it to W2 (s) as shown in FIG. 4.

Step 3: In this embodiment, in order to evaluate two transfer function characteristics, the weighting functions W1 (s) and W2 (s) specified in step 2 are multiplied by Ger(s) and Gu2r (s), respectively. Let the evaluation function be the H∞ norm of the weighted transfer function shown below.

[0025]

[Equation 3] The evaluation function can be determined by the above procedure. In this example, two transfer functions Ge are used to evaluate the control characteristics.
r(s) and Gu2r(s), but even if more characteristics are included in the evaluation, the evaluation function J may be set in exactly the same manner. Furthermore, if the controlled object 1 is a multi-input/output system, the H∞ norm is also defined for matrix functions, so the above procedure is exactly the same.

The feedforward control constant calculation means 5 calculates the evaluation function J determined by the evaluation function determination means 6.
The control constant K4 (s) of the feedforward control calculation means 4 is determined such that J≦ε .

That is, as mentioned above, Ger(s) and Gu2r(s) can also be expressed as functions of the control constant K4 (s), and therefore J is the control constant KG4 (
s). Therefore, the optimum K4 (s) can be determined using equation (6).

Examples of methods used for H∞ norm optimization include Systems & Control.
Letters (Vol.11, 167/172, 19
There is a method published in 88). After obtaining the expanded system from equation (2) and realizing the state space, the control constant K4 (s) of the feedforward control calculation means 4 can be obtained by solving two Riccati-type matrix equations. However, if you want to configure the control device to satisfy equation (6), depending on the value of ε, the optimal control constant K4 (s
) may not exist. In that case, return to step 2, change the setting of the weighting function, and repeat the same procedure to obtain the optimal control constant K4 (s).

Next, the feedforward control calculating means 4 calculates the manipulated variable u2 (t) to be input to the controlled object 1 from the target value r(t). In this case, the calculation algorithm and the control constant K4 (s) are determined by calculation in the feedforward control constant calculation means 5 based on the evaluation function set by the evaluation function determination means 6 as described above.

Specific Examples Next, specific examples of the present invention will be explained. A specific example is one in which the attitude control system of a flexible structure satellite is controlled.

The controlled object is an infinite-dimensional vibration system, and the transfer function of the controlled object approximated by the first-order vibration mode is

003
2]

[Equation 4] Using equation (7) as a design model, this controlled object is controlled by the two-degree-of-freedom control device according to the present invention. First, for the feedback control calculation means, feedback control constants were determined using the H∞ optimal control theory based on the mixed sensitivity problem as is. Regarding the feedforward control calculation means, as in the embodiment, the transfer functions Ger(s) and Gu2r(s) representing the target value tracking characteristic and the restriction of the manipulated variable are evaluated, and the weighting function is

[0033]

The feedforward control constant K4 (s) was determined as follows. FIG. 6 shows the output response of the controlled object to the target value r(t)=1. As shown in FIG. 6, a two-degree-of-freedom control system that can obtain a good response has been realized with little trial and error.

[0034]

As explained above, according to the present invention, in the evaluation function determining means, an appropriate transfer function related to the feedforward control calculation means is specified to determine the evaluation function.
Since the feedforward control constant is determined by the feedforward control constant calculating means, control can be performed more quickly and accurately than when the control constant is determined by trial and error.

[Brief explanation of the drawing]

FIG. 1 is a schematic system diagram showing an embodiment of a two-degree-of-freedom control device according to the present invention.

FIG. 2 is a detailed diagram of feedback control calculation means.

FIG. 3 is a diagram showing a σ plot of the weighting function W1.

FIG. 4 is a diagram showing a σ plot of weighting function W2.

FIG. 5 is a flow diagram showing the operation of the two-degree-of-freedom control device according to the present invention.

FIG. 6 is a diagram showing an output response of a controlled object in a specific example of the present invention.

[Explanation of symbols]

1 Controlled object 2 Feedback control calculation means 3 Feedback control constant calculation means 4 Feedforward control calculation means 5 Feedforward control constant calculation means 6 Evaluation function determination means

Claims (4)

[Claims] 1. Feedback control calculation means for calculating a manipulated variable to be applied to a controlled object from a control output signal and a target input signal, feedback control constant calculation means for calculating a feedback control constant used in the feedback control calculation means, and a target input signal. a feedforward control calculation means for calculating a manipulated variable to be applied to a controlled object from a signal; a feedforward control constant calculation means for calculating a feedforward control constant used in the feedforward control calculation means; and an evaluation function determining means for specifying a transfer function and calculating an evaluation function for this transfer function, and the feedforward control constant calculating means sets the evaluation function determined by the evaluation function determining means to a minimum value or a tolerance value or less. A two-degree-of-freedom control device characterized in that a feedforward control constant is determined as follows. 2. The evaluation function determining means takes a function obtained by multiplying a suitable transfer function by a weighting function, and takes the norm of this function as the evaluation function. Degree of freedom control device. 3. The two-degree-of-freedom control device according to claim 2, wherein the evaluation function determining means uses an H∞ norm or an H2 norm as the norm of the function. Claim 4: The evaluation function determining means determines the appropriate transfer function by G.
1 (s),...Gn (s), and the weighting functions applied to each transfer function are defined as W1 (s),...Wn (s), the evaluation function is set to [Equation 1]. The two-degree-of-freedom control device according to claim 2.