Design Theory Of Satisfactory PID Controller

The proportional, integral, and derivative (PID) control algorithm is the most widely used control strategy in industrial control systems. In the latest several decades the interest among academics of PID control is large and increasing. There are three questions which are urgently desired to be answered due to the drawback of the traditional PID tuning methods. The first question is the consistency of the desired performance index set of PID control system (whether there exists a PID controller satisfying the required multiple performance specifications). How to construct the theory of calculating the PID controllers when the desired performance index set is consistent is the second question. The last question is how to compute the whole consistent solution set (the satisfactory solution set) via a visible technique and how to select the desired satisfactory solutions in the whole consistent solution set. An efficient and suitable to the occasion method to answer the above three questions is presented in this thesis.In the first place, using the idea of satisfactory control and the consistency theory of desired index set, three types of single-input single-output systems, namely, n-order linear time invariant systems, n-order linear time invariant systems with time delay and n-order linear time invariant stochastic systems under PID control, are considered in the thesis. The consistency of the desired performance index set consists of the whole or parts of the following indexes, such as regional pole constraints index, dynamic error coefficient index, disturbance attenuation H_∞ index, robustness index, control cost index, variance index and opportunity-awaiting characteristic index including the average residence time index and the average waiting time index, is considered. The sufficient condition of existing a PID controller satisfying the above desired performance index is proposed. Secondly, the theorems and corollaries of calculating the PID controller parameter set satisfying the corresponding desired performance index are derived, respectively. Finally, the visible; technique of calculating the consistent solution set in the PID controller parameter space based on a graphical approach is proposed. The visible technique of computing the whole set is constructed based on plotting the boundaries of the PID controller parameter set satisfying the each desired performance index in the PID controller parameter space.The theoretical analysis and simulation results show that the most significant features of the proposed satisfactory PID controller design method in this thesis are as followings: First,according to the consistent region, the existence condition of a PID controller...