It is generally difficult to design feedback controls of nonlinear systems with time delay to meet time domain specifications such as rise time, overshoot, and tracking error. Furthermore, these time domain specifications tend to be conflicting to each other to make the control design even more challenging. This paper presents a cell mapping method for multi-objective optimal feedback control design in time domain for a nonlinear Duffing system with time delay. We first review the multi-objective optimization problem and its formulation for control design. We then introduce the cell mapping method and a hybrid algorithm for global optimal solutions. Numerical simulations of the PID control are presented to show the features of the multi-objective optimal design.
Xiong F, Qin Z, Hernández C, Sardahi Y, Narajani Y, Liang W, Xue Y, Schütze O, Sun J. A multi-objective optimal PID control for a nonlinear system with time delay. Theoretical and Applied Mechanics Letters. 2013 Jan 1;3(6):063006.