PID and PID-like controller design by pole assignment within D-stable regions

This paper presents a new PID and PID-like controller design method that permits the designer to control the desired dynamic performance of a closed-loop system by first specifying a set of desired D-stable regions in the complex plane and then running a numerical optimisation algorithm to find the controller parameters such that all the roots of the closed-loop system are within the specified regions. This method can be used for stable and unstable plants with high order degree, for plants with time delay, for controller with more than three design parameters, and for various controller configurations. It also allows a unified treatment of the controller design for both continuous and discrete systems. Examples and comparative simulation results are pro-vided to illustrate its merit

A hybrid global optimization method: The multi-dimensional case

AbstractWe extend the hybrid global optimization method proposed by Xu (J. Comput. Appl. Math. 147 (2002) 301–314) for the one-dimensional case to the multi-dimensional case. The method consists of two basic components: local optimizers and feasible point finders. Local optimizers guarantee efficiency and speed of producing a local optimal solution in the neighbourhood of a feasible point. Feasible point finders provide the theoretical guarantee for the new method to always produce the global optimal solution(s) correctly. If a nonlinear nonconvex inverse problem has multiple global optimal solutions, our algorithm is capable of finding all of them correctly. Three synthetic examples, which have failed simulated annealing and genetic algorithms, are used to demonstrate the proposed method

A Trust-Region Approach to Nonlinear Systems of Equalities and Inequalities

In this paper, two new trust-region algorithms for the numerical solution of systems of nonlinear equalities and inequalities are introduced. The formulation is free of arbitrary parameters and possesses sufficient smoothness to exploit the robustness of the trust-region approach. The proposed algorithms are one-sided least-squares trust-region algorithms. The first algorithm is a single-model algorithm, and the second one is a multi-model algorithm where the Cauchy point computation is a model selection procedure. Global convergence analyses for the two algorithms are presented. Our analysis generalizes to nonlinear systems of equalities and inequalities the well-developed theory for nonlinear least-squares problems. Numerical experiments on the two algorithms are also presented. The performances of the two algorithms are reported. The numerical results validate the effectiveness of our approach