JPH06324711A - Design system device for mechanism control system - Google Patents

Abstract

PURPOSE:To realize the mechanism control system satisfying a design specification efficiently in a shorter time than that for a conventional device by grasping equations of motion of a mechanism and its control characteristic altogether and selecting an overall characteristic as a design parameter satisfying an object function and a control condition. CONSTITUTION:When an objective design specification is given, the specification is expressed in equations and a function generating section 50 gives data to a general-purpose optimization arithmetic operation section 51 as an objective function and restriction condition. On the other hand, A mechanism system numeral model 53 and a control system numerical model 54 are used to set an entire system model 52 and the data are given to the general-purpose optimization arithmetic operation section 51. The general-purpose optimization arithmetic operation section 51 obtains an optimum parameter and a response arithmetic operation section 58 calculates a behavior by using the parameter. A numeral model revision section 55 corrects the data when a specification satisfaction discrimination section 56 does not satisfy the result, and the processing is repeated till the result is satisfied. When a solution satisfying the condition is in existence, a control system decreasing an evaluation function among solutions obtained by a nonlinear programming 7 is selected.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a mechanism control system design system apparatus and method, and more particularly to a mechanism control system using a computer in designing a mechanism apparatus such as a semiconductor manufacturing apparatus or a robot manipulator which requires high precision positioning. The present invention relates to a design system device for optimally selecting system and control system design parameters.

[0002]

2. Description of the Related Art Conventionally, in designing a mechanical system, the link members constituting the mechanism have been considered as rigid bodies and their behaviors have been analyzed. However, when attempting to reduce the weight of the mechanical system, the rigidity of the link member becomes insufficient, and it may not be considered as a rigid body. In addition, if high-speed and high-accuracy positioning is performed, it is necessary to consider minute vibrations that have been ignored so far. Therefore, it is necessary to analyze the link flexibility. In an attempt to solve these problems, DAs have been used to simulate mechanical systems.
DS (Dynamic Analysis and Design System) and ADA
MS (Automatic Dynamic Analysis of Mechanical Syst
em) The program is commercially available. However, these programs are for predicting the dynamic behavior, and the design values of the mechanism and the control are given in advance, and the optimum design parameters that satisfy the objective function and the constraint conditions cannot be obtained. In addition, control performance deteriorates due to interference between the mechanical system and the control system caused by the recent trend toward lighter and more compact mechanical systems, or higher speed and higher accuracy.Therefore, there is an increasing demand for simultaneous design of the mechanical system and the control system. Is coming. For the simultaneous optimal design of mechanism and control system, Proceedings of the Society of Instrument and Control Engineers, Vol. 26, No. 10, 1140 to 114.
It is described on page 7, and the sensitivity analysis is used to decide the change of design parameters. The control law is based on optimal control theory. Proceedings of the Japan Society of Mechanical Engineers, Vol.55, No.519,
From page 2777 to page 2783, basically sensitivity analysis,
This is a design method based on the linear control law. Other papers on simultaneous optimization of mechanical system and control system have been published, but the ones dealt there are mainly the combination of minimum weight and optimum regulator. Moreover, general-purpose software for simultaneous optimal design of mechanical system and control system has not been found yet.

[0003]

In the above prior art, when design parameters such as the shape of the mechanism and control gains are given, numerical modeling can be performed to simulate the dynamic behavior. I don't know if it is the optimum value that satisfies the target specifications. In addition, the method using the sensitivity analysis described above is difficult to use when the objective function and constraint conditions cannot be differentiated, and if the design specifications become strict, it may not be possible to deal with the linear control law alone. Out. Further, in the structural system, only the member parameters are changed, and the structure itself is not changed, so that the satisfactory design specifications are limited.

An object of the present invention is to collectively grasp the motion equations and control characteristics of a mechanism so as to use it as a tool for developing an optimum mechanism and control system, and to evaluate the comprehensive characteristics by objective function and constraint conditions. It is an object of the present invention to provide a mechanism control system design system device and method for simultaneously optimizing a mechanism design and a control design that can be selected as a design parameter that satisfies the above and can be simulated using these values.

[0005]

In order to solve the above problems, the present invention has the following constitution.

(1) In a mechanism control system design system device for constructing a mechanism system calculation model and a control system calculation model in a system and calculating the response of the entire system using the mechanism control system calculation model, From the function generation unit that generates a function with the target design specification as an evaluation function and a constraint condition, the arithmetic processing unit that automatically changes the control parameters of the control system calculation model, the evaluation function, the constraint condition, and the mechanism system calculation model. A general-purpose optimizing calculation unit that calculates optimum control parameters and a determination unit that processes whether or not the target design specifications are satisfied are provided, and the control parameters are automatically obtained so as to satisfy the target design specifications.

(2) A function of selecting a morphology generator of the control system according to the result of the judgment unit which has a morphology generator of the linear control system and a morphology generator of the non-linear control system and processes the satisfaction of the target design specifications. Is equipped with.

(3) When a solution does not exist in the linear control system configuration routine in the above design apparatus, the objective function and the constraint conditions are changed, the model is changed, and the design choices by the non-linear control method are provided so that the design specifications are satisfied. Is provided with a means for changing the value.

(4) A response analysis operation unit is provided, and it is determined from the obtained results whether or not the design specifications are satisfied. If the specifications are not satisfied, the structural system is changed based on the knowledge base. A means for changing the value so as to satisfy the design specifications by repeating the above calculation is provided.

[0010]

In the mechanism control system design system device and method, the objective function and constraint conditions of the mechanism system are first determined from the design specifications. A nominal model is derived from this mechanical system, a linear control system is constructed based on this model, and a closed-loop transfer function is derived. The transfer function of the closed loop system is transformed by using the control design parameter function, and the control parameter is determined by obtaining the design parameter by the nonlinear programming together with the transfer function, the objective function and the constraint condition. If no solution exists,
The objective function and constraints are changed, or the mechanical system parameters are changed, and the process is repeated until a solution exists. If a solution exists, a response analysis is performed to check whether the design specifications are satisfied. If not, the mechanical system parameters are changed and the calculation is repeated from the beginning. If the specifications are satisfied, the values of the objective function are compared with the values obtained so far, and if the values are smaller, the mechanical system parameters are updated, and if the values are not smaller, the parameters that minimize the objective function are saved, and the processing ends. By taking this measure, it is possible to more efficiently design the mechanism control system that can obtain a better response.

[0011]

An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram showing an embodiment of a mechanism control system design system device according to the present invention. In FIG. 1, the present apparatus includes a function generation unit 50 for an objective function and a constraint condition, a general-purpose optimization calculation unit 51, an overall system numerical model unit 52, a mechanical system numerical model unit 53, a control system numerical model unit 54, and a numerical model changing unit. 55, specification satisfaction determination unit 56, result output display unit 5
7 and a response calculation unit 58. When the target design specification is given, this specification is expressed by a mathematical expression and data is passed from the function generating section 50 to the general-purpose optimizing calculation section 51 as an objective function / constraint condition. On the other hand, the whole system numerical model 52 is assembled using the mechanical system numerical model 53 and the control system numerical model 54, and the data is passed to the general-purpose optimizing calculation unit 51. The general-purpose optimization calculation unit 51 obtains optimum design parameter values, and the response calculation unit 58 uses these values to calculate the behavior. If the specification satisfaction determination unit 56 does not satisfy the specification, the numerical model modification unit 55 corrects the data and repeats until it is satisfied. If satisfied, output the results. FIG. 2 is a flow showing an example of an algorithm of the mechanical / control system simultaneous design apparatus. When the design specification 1 is given in the figure, this is mathematically expressed and expressed as an objective function / constraint condition 2. Further, from the design specification 1, a mechanical system 3 that enables this is generated, its equation of motion is derived, and a linearized nominal model 4 is obtained based on this equation of motion. With respect to this nominal model, a nominal linear control system 5 is calculated by known LQ control, H∞ control law, and the like. A closed loop system is formed by the control system that adds the nominal model and the control system design parameter, and the value of the optimum design parameter is calculated by the nonlinear programming method 7 by the closed loop system transfer function, the objective function and the constraint condition 2, and the condition is satisfied. Check if a solution exists.
If there is a solution, a control system that reduces the evaluation function is selected from the solutions obtained by the nonlinear programming method 7, and the response analysis is performed using the whole system numerical model in combination with the original mechanical system 3.
As a result of this response analysis, if the design specifications are not satisfied,
Change the mechanical system based on the knowledge base 14
Return to and repeat the same calculation. If the response analysis satisfies the design specifications, the process goes to the objective function comparison unit 15, and if the value of the objective function becomes larger than the previous value, the process ends. However, when the number of loops is small and the processing is terminated, the objective function may not be sufficiently small, and thus iterative calculation is performed a certain number of times or more. If there is no solution in the nonlinear programming method, one is selected from the options of 10 when changing the objective function / constraints and 11 when designing using the nonlinear control system, and a satisfactory result is obtained. Repeat the calculation until you get it. If the solution that satisfies the design specifications is not obtained even after reaching the set number of iterations, the calculation is stopped and it is displayed that the mechanism control system that satisfies the given design specifications cannot be obtained.

The algorithm described above is, for example,
The following method can be used. First, the mechanical design. The equation of motion of the mechanical system can be described by the following equation.

[0014]

[Equation 1]

Here, M, D, and K are a mass matrix, a damping matrix, and a stiffness matrix, respectively, q is a displacement vector, and Q is an external force vector acting on the system. Here, it is assumed that the external force vector Q can be written as follows by the control input u and the disturbance vector f as shown in Equation 2.

[0016]

[Equation 2] Q = Uu + Ff (Equation 2) Here, U and F are coefficient matrices of each vector.

Among the structures satisfying a given design condition, in order to obtain the structure most suitable for a certain purpose, that is, the optimum structure, the problem of determining the parameter values of the mechanical system is generally called "optimal design". It is called "problem".

The n design parameters whose values are to be determined are

[0019]

Equation 3] _{b = {b 1, b 2} , ...... b N} ... When equation (3), the optimal design problem is generally formulated in the following form.

K constraint expressions

[0021]

## EQU00004 ## A design that minimizes (maximizes) the objective function f (b) among the design variables that satisfy g (b) .gtoreq.0 (j = 1, 2, ..., K) (Equation 4). variable

[0022]

## EQU5 ## The problem is to find b = {b ₁ , b ₂ , ..., B _N } ... (Equation 5). "Variable design variables (structural shape, plate thickness, material, etc.) and constraint conditions (stress, displacement, natural frequency, etc.)
Is less than or equal to a certain value (or more, same)
Stress, displacement, etc.) is minimized (maximized). "It becomes a problem. The design variables mainly used are the member dimensions (plate thickness, length,
Width), shape, and geometrical arrangement. The constraints are stress, displacement, acceleration, natural frequency, buckling load, weight, and energy. The objective functions are stress, displacement, acceleration, natural frequency, buckling load, weight and energy. Number 1, M, D, K, Q
Is a function of the design variable b. In many cases, the number of parameters that minimizes (maximizes) the objective function f (b) under the constraint of the mathematical expression 3 is 5 and the method in the mathematical programming is used by utilizing a computer.

Next, the optimum control problem will be described. Control system design is to obtain a desired result by adding a control system for controlling vibration and motion of a mechanical system. The control law design problem can be expressed as follows. “When a control target is given, types and arrangements of sensors and actuators are given, and design specifications are given, finding control rules that satisfy these design specifications, or that such control rules do not exist. To find. There are a method of designing based on a transfer function expression and a method of designing based on a state space expression to obtain such a control law. There is LQ control as a method based on the state space expression, which is often used when optimizing the control system. Here, we describe an optimization method based on the transfer function expression that can handle various design specifications. First, a generalized plant required in this method will be described. The signal entering the controlled object P ₀ is divided into two. The actuator signal u generated by the controller and other external input signals are w
And Similarly, the signal output from the controlled object P ₀ is also divided into two signals. The signal observed by the sensor is y, and the controlled variable is z. This allows

[0024]

[Equation 6]

P represented by is called a generalized plant and can be represented as shown in FIG. Now consider the control system with one degree of freedom shown in FIG. This is a conventional feedback system expression method. We will show how to make this a generalized plant representation. Here, r is a target value signal, n _p is noise added to the actuator, n _s is sensor noise, and yp is an output from the control target. External input vector w

[0026]

[Equation 7]

And the controlled variable z is

[0028]

[Equation 8]

Then, the generalized plant P is as follows.

[0030]

[Equation 9]

A generalized plant representation of this one-degree-of-freedom control system is as shown in FIG. The closed loop transfer function is as follows.

[0032]

[Equation 10]

The transfer matrix of this generalized plant is necessary when the design specifications are expressed by mathematical expressions.

Next, some examples will be given below as design specifications of the control system, and their mathematical expressions will be shown. However, the vector and matrix used there are defined as follows.

[0035]

[Equation 11]

[0036]

[Equation 12]

[0037]

[Equation 13]

As the asymptotic followability of the step response specification,

[0039]

Iim s (t) = Hcc (0) = 1 (Equation 14) t → ∞ (s (t) is the step response of Hcc) As overshoot and undershoot,

[0040]

## EQU15 ## φos (Hcc) = sup s (t) -1 (Equation 15) t ≧ 0

[0041]

[Equation 16] φus (Hcc) = sup-s (t) (Equation 16) t ≧ 0 As rise time and settling time,

[0042]

Φrise (Hcc) = inf {T | s (t)> 0.8 for t ≧ T} (Equation 17)

[0043]

Φsettle (Hcc) = inf {T || s (t) -1 | <0.05 for t ≧ T} (Equation 18) As the tracking error specification,

[0044]

[Equation 19] Tracking error: etrk = zc−wc Htrk: transfer function from command wc to etrk || Htrk || ≦ α (Equation 19) As a regulation specification,

[0045]

[Equation 20] Considering the influence of wd on zc, Hcd is reduced.

|| Hcd || ≦ α (Equation 20) It is assumed that the variation Δ of the controlled object is given as the robust stability as follows.

[0047]

[Equation 21]

At this time, in order for the system to be robustly stable, the closed-loop transfer matrix should satisfy the condition of Eq.

[0049]

[Equation 22]

Although it has been shown that the closed-loop transfer matrix plays an important role in expressing the design specifications by mathematical expressions, a method of transforming the equation 10 into a form suitable for the nonlinear programming will be shown. In number 6

[0051]

[Equation 23]

When a closed loop system transfer function from w to z is obtained,

[0053]

[Number 24] Hzw = Pzw-PzuK (1 + PyuK) ~ 1 Pyw ... is (number 24).

The stabilizing compensator K can be expressed by using the irreducible expression of Pyu.

[0055]

[Equation 25]

By substituting this into Eq. 24 and rearranging, Eq. 26 is obtained.

[0057]

[Equation 26]

From equation 1, the transfer function P ₀ of the controlled object is

[0059]

[Equation 27]

And obtain the observation equation

[0061]

By setting y = Cx (Equation 28),

[0062]

[Equation 29] P ₀ = C (sl−A) to ¹ B (Equation 29)

Based on the above, the optimization problem of the control system can be described as follows.

[0064]

[Equation 30]

Φ is a convex evaluation function, and K is a convex set satisfying the constraint condition. Since Q is infinite as it is,

[0066]

[Equation 31]

The optimum parameter hi is calculated by a non-linear programming method by approximating Here, hi is a real number and Qi is a fixed and stable transfer function. This makes it possible to know whether or not there is a linear control system that satisfies the design specifications.

An example using the mechanism / control system simultaneous optimization algorithm of the present invention will be shown. The transfer function of the target plant is P
_{If 0} and the controller are K, the block diagram is as shown in FIG. n _p and n _s represent noise, and r is a target value. The control amount z and the exogenous signal w are determined as follows.

[0069]

[Equation 32]

The closed loop system transfer function Hzw is expressed as follows.

[0071]

[Expression 33]

As the evaluation function J, a general one is adopted as follows.

[0073]

[Equation 34] J = || H ₁₁ || ₂ ² + r ₁ || H ₁₂ || ₂ ² + r ₂ || H ₂₃ || ₂ ² (Equation 34) The control target is a spring as shown in FIG. -Consider a mass-damper system. The equation of motion of this system is as follows.

[0074]

[Equation 35]

Let us assume that the transfer function of this system is P ₀ and control is performed by the controller K of the one-degree-of-freedom system. Y in FIG.
The following relational expression holds for y _p .

[0076]

[Equation 36]

The control amount z and the exogenous signal w are determined as shown in equation 32. Then, the equation of state of this system becomes as follows.

[0078]

[Equation 37]

[0079]

[Equation 38]

From the equation 26, the closed loop transfer function Hzw is

[0081]

It can be written that Hzw = T ₁ + T ₂ QT ₃ (Equation 39), and T ₁ , T ₂ , and T ₃ can be calculated as follows.

[0082]

[Formula 40]

The following constraint conditions are adopted in the control system design specifications.

The step response is s (t).

[0085]

[Formula 41]

The parameter Q is

[0087]

[Equation 42]

It was set as Also, as a constraint condition of the mechanical system,

[0089]

43 is set as 0.5 ≦ m ≦ 1.5 (Equation 43).

FIG. 7 shows the result of calculation based on the above. When m = 0.5, the objective function J becomes minimum,
A solution satisfying the constraint conditions was obtained. As can be seen from FIG. 7, the constraint condition is satisfied.

[0091]

According to the present invention, it is possible to determine each design parameter while considering both dynamic characteristics of the mechanical system and the control system. A satisfactory mechanism control system can be constructed.

[Brief description of drawings]

FIG. 1 is a flowchart showing an embodiment of the present invention.

FIG. 2 is a flowchart of an algorithm according to an embodiment of the present invention.

FIG. 3 is a block diagram of a generalized plant.

FIG. 4 is a block diagram of a conventional feedback representation.

FIG. 5 is a block diagram of a one-degree-of-freedom system generalized plant.

FIG. 6 is an explanatory diagram of a control target.

FIG. 7 is an explanatory diagram of a calculation result obtained by the algorithm of the present invention.

[Explanation of symbols]

50 ... Function generator, 51 ... General-purpose optimization calculation section, 52 ... Numerical model of entire system, 53 ... Numerical model of mechanical system, 54 ... Numerical model of control system, 55 ... Numerical model change section, 56 ... Satisfaction determination section, 57 ... Output display section, 58 ... Response analysis section.

Claims (1)

[Claims] 1. A mechanism control system design system apparatus for constructing a mechanism system calculation model and a control system calculation model in a system, and calculating the response of the entire system using the mechanism control system calculation model A function generator that generates a function with the design specifications as an objective function and constraint conditions, an arithmetic processing unit that automatically changes the control parameters of the control system calculation model, and an optimum from the objective function, constraint conditions, and mechanism system calculation model General-purpose optimization calculation unit that calculates various control parameters,
A mechanism control system design system device, comprising: a determination unit for processing whether or not a target design specification is satisfied, and automatically determining the control parameter so as to satisfy the target design specification.