(A) systematic design method and its stability analysis for PID control for a class of nonlinear systems

Abstract

This thesis deals with a systematic design method and its stability analysis for PID conrol for a class of MIMO (Multi-Input Multi-Output) nonlinear systems which can be expressed as companion form (phase variable form) such as robot manipulators and shows results of application of them to robot manipulators. This method incorporates the number of tuning gains, far less than those for conventional PID control design methods. To this end, above all, we show that under some conditions the PID control is equivalent with Time Delay Control (TDC), which is well known robust control method for nonlinear systems with uncertainty, for nonlinear systems of companion form in discrete domain. Nowadays many digital devices like Mciroprocessor, DSP, and so on are used as harward of control system. In these digital devices, PID control is implemented discretely. Therefore considering discrete PID control is more realistic and practical. Using the equivalent relationship between them, a systematic design method for PID control is suggested. The PID gains obtained by suggested design method have robust property due to robustness of TDC. For a stability analysis of the suggestd design method for PID control, first of all, the stability of the closed loop system with discrete TDC is achieved. TDC implemented in digital devices is discrete and a system is continous so the closed loop system becomes a sampled data system. Hence in viewpoint of the sampled data system, we analyze a stability of a closed loop system. Then using results of the stability analysis of discrete TDC and the equivalent relationship between PID control and TDC, a stability of the suggested design method for PID control are analyzed. From the stability analysis, a guideline that could be used for design of PID control is suggested. A sampling time interval of control system and TDC parameters which are necessary to design PID control affect the stability. To use the guideline, it needs to know ...