Abstract:
Proportional-integral-derivative (PID) controllers have been widely used in automatic control systems. In this thesis, we consider the problems of synthesizing PID controllers which guarantee robust stability and performance for single-input single-output (SISO) plants in the presence of model uncertainty. It is previously shown that this problem can be translated to simultaneous stabilization of the closed-loop characteristic polynomial and a family of complex polynomials. For a fixed proportional gain, integral and derivative gain values can be constructively determined using linear programming. The most important feature of this method is that it computationally characterizes the entire set of the admissible PID gain values. This research work also provides an algorithum of poilynomial stabilization. In particular, MATLAB programs are developed to design appropriate PID parameters. We verify design results on sample problems spanning from nominal stability to robust stability and performance. The computer programs employ the unified and systematic approach using polynomial stabilization. Subsequently, we apply the developed programs to design PID controllers for a laboratory-scale belt conveyor system. Based on the dynamical model and its uncertainties, we characterize admissible regions satisfying nomincal stability and robust performance. The admissible regions of PID gains are shown both in 2D plot at specified value of k[subscript p], and in 3D plot for various values of k[subscript p]. The computer simulations confirm that the chosen PID robust controller yields satisfactory nominal and robust performance. Comparing the design result with the well-known Ziegler-Nichols method. It is observed that the PID controller by Ziegler-Nichols method is quite close to the boundary of the admissible region obtained from this work. Hence, the developed computer programs provide a viable and practical means for robust PID tuning.
