In this work a multivariable optimal PID controller for a continuous stirred tank reactor was designed in order to obtain optimal system performance without decoupling. The tuning of this controller is obtained by using an evolutionary algorithm (MAGO). This solution is compared with classical methods for multivariable control. The results of this study showed that the controller designed rejects the effect of disturbances and follows the external reference signal efficiently. Evolutionary tuning overcomes broadly the classical methods.

In this chapter, it is demonstrated that when using advanced evolutionary algorithms, whatever the adopted system model (SOSPD, nonminimum phase, oscillatory or nonlinear), it is possible to find optimal parameters for PID controllers satisfying simultaneously the behavior of the system and a performance index such as absolute integral error (IAE). The Multidynamics Algorithm for Global Optimization (MAGO) is used to solve the control problem with PID controllers. MAGO is an evolutionary algorithm without parameters, with statistical operators, and for the optimization, it does not need the derivatives, what makes it very effective for complex engineering problems. A selection of some representative benchmark systems is carried out, and the respectively two-degree-of-freedom (2DoF) PID controllers are tuned. A power electronic converter is adopted as a case study and based on its nonlinear dynamical model, a PI controller is tuned. In all cases, the control problem is formulated as a constrained optimization problem and solved using MAGO. The results found are outstanding.