Design of Optimal PID Controller withɛ-Routh Stability for Different Processes

This paper presents a design method of the optimal proportional-integral-derivative (PID) controller withɛ-Routh stability for different processes through Lyapunov approach. The optimal PID controller could be acquired by minimizing an augmented integral squared error (AISE) performance index which contains control error and at least first-order error derivative, or even may containnth-order error derivative. The optimal control problem could be transformed into a nonlinear constraint optimization (NLCO) problem via Lyapunov theorems. Therefore, optimal PID controller could be obtained by solving NLCO problem through interior method or other optimization methods. The proposed method can be applied for different processes, and optimal PID controllers under various control weight matrices andɛ-Routh stability are presented for different processes. Control weight matrix andɛ-Routh stability’s effects on system performances are studied, and different tuning methods’ system performances are also discussed.ɛ-Routh stability’s effects on disturbance rejection ability are investigated, and different tuning methods’ disturbances rejection ability is studied. To further illustrate the proposed method, experimental results of coupled water tank system (CWTS) under different set points are presented. Both simulation results and experiment results show the effectiveness and usefulness of the proposed method.

Interior methods for constrained optimization

Interior methods for optimization were widely used in the 1960s, primarily in the form of barrier methods. However, they were not seriously applied to linear programming because of the dominance of the simplex method. Barrier methods fell from favour during the 1970s for a variety of reasons, including their apparent inefficiency compared with the best available alternatives. In 1984, Karmarkar's announcement of a fast polynomial-time interior method for linear programming caused tremendous excitement in the field of optimization. A formal connection can be shown between his method and classical barrier methods, which have consequently undergone a renaissance in interest and popularity. Most papers published since 1984 have concentrated on issues of computational complexity in interior methods for linear programming. During the same period, implementations of interior methods have displayed great efficiency in solving many large linear programs of ever-increasing size. Interior methods have also been applied with notable success to nonlinear and combinatorial problems. This paper presents a self-contained survey of major themes in both classical material and recent developments related to the theory and practice of interior methods.