A Design Method of Robust PID Control by Using Backstepping Control with Time Delay Estimation and Nonlinear Damping

Abstract

This thesis presents a design method of robust Proportional-integral-derivative (PID) control by using backstepping control with time delay estimation (TDE) and nonlinear damping. PID controllers are widely used as feedback control in many industrial control system fields. The structure of a PID control is simple and consists of three terms that include a proportional gain, an integral gain and a differential gain. The control makes its desired output by assigning PID gains that are required to control systems precisely after calculating the error between the desired input and output of systems. Gains of PID control have definite physical meaning. If these gains are tuned carefully, acceptable performance can be obtained since steady-state error and transient response are improved simultaneously. To select PID gains, many previous studies investigated methods of tuning PID control gains to get good performance. Methods of tuning gains are selected on the analytical basis of closed-loop stability and performance. Since PID controllers are linear models and many studies deal with linear plants, it is very difficult to select PID gains for nonlinear plants. Although many previous studies have been conducted such as Fuzzy control and optimal control, the methods proposed in these studies are very difficult and theoretically complex. As a result, PID gains are usually tuned heuristically. A systematic method was proposed by Chang et al. to select gains of robust PID control for nonlinear plants by using second-order controller canonical forms in discrete PID controllers from the viewpoint of a sampled-data system. In that study, although the plant model was unknown, the method was enabled to determine robust PID gains by using time delay control (TDC) when the plant has second-order controller canonical form and when TDC and PID controls are conducted in discrete time domain. Due to the equivalence to TDC, the gains of PID control were determined.TDC is a simple and effective technique for estimating system nonlinearities and uncertainties. This method uses the time delayed signal of system variables to estimate uncertainties of a system. While TDC has the advantage of requiring no prior knowledge of the system model, it also has the disadvantage of time delay estimation (TDE) error due to hard nonlinearities. It degrades the system stability and performance. When PID gains are tuned by using TDC with a system that has hard nonlinearities, system stability and performance cannot be guaranteed. To overcome TDE error and guarantee the stability of a system,backstepping control with TDE and nonlinear damping was proposed. Based on this method, in this paper, the equivalent relationship between PID control and backstepping control with TDE, nonlinear damping will be presented to select PID gains efficiently. While general PID controllers have constant gains, the proposed PID controller has variable PID gains due to nonlinear damping that uses the feedback state. In addition, the gains of the proposed PID control will be analyzed to identify the characteristics of the purposed controller. Since the proposed PID control uses the equivalent control method by backstepping control with TDE and nonlinear damping, it has the enhanced control performance and stability with respect to the difficulties presented above. ⓒ 2013 DGIST