Gain Scheduling PID Controller via Least Squares Optimization

Usually the industrial plants are modelled in a nominal situation and then the controller is designed based on it. However, the dynamics of industrial plants are generally dependents of parameters, which can change or even can not be properly estimate until a final implementation. In this paper, it is proposed an adaptive PID controller to work around with parameter variations and pursue a nominal designed condition. The problem is modeled as a linear system, where the gains of the PID controller are the variables of interest, then the stability constraints are imposed on the system. As the linear system to be solved is over-determined, the least squares method was used and it was implement as a quadratic optimization problem. Besides, the stability in case to switch the controller during the operation is also covered and a set of numerical examples are presented including a simulation on PSIM software.