Numerical Optimization of PID-Regulator for Object with Distributed Parameters

Abstract

The control of dynamic objects is very important for technologies and technical sciences. The difficulty of the control depends on the complexity of object mathematical model. Objects with distributed parameters are most difficult for control with feedback loop. The mathematical model of such object is much more complicated. There are two method of calculating regulator. The first method is analytical calculation of the coefficients. It can be used only for relatively simple object. The second method is numerical optimization. It can be used even with complex object. But object with distributed parameters has such complex model that in this case the use of the method of numerical optimization is a difficult problem. Only approximate model of such object can be used for the optimization with the help of the simulation program. Newest results in numerical optimization are based on some specific cost functions. Various composite cost functions are effective tools for regulator calculation. But even these tools are not sufficient. The paper researches possibilities of the use of approximate mathematical model of objects with distributed parameters and various cost functions, including new ideas, for the calculation of the regulator for system with such object. With all known methods, it was impossible to reduce the overshooting less than 22%. The proposed new cost function allows reducing of the overshoot to a value of about 11%, which is be preferred for many applications. The proposed method adds an arsenal of techniques of control of complex dynamic objects.