Linear Quadratic Optimal Robust Multivariable Proportional-Integral Control Design for a Boiler-Turbine Unit

Boiler-turbine unit is a highly nonlinear, coupled, and ill-conditioned system. Moreover, the presence of physical constraints, such as actuator magnitude and rate limits, makes the system difficult to control. This paper employs a fixed multivariable proportional-integral (PI) controller of the I-P structure for robust linear quadratic (LQ) compensation of a nonlinear boiler-turbine benchmark. In order to ensure that a single PI controller works for the whole operating region of this nonlinear system, the linearized model of the system is represented as a norm-bounded, time-varying uncertain system. The ranges of the uncertain parameters of this linearized model are determined from different operating points of the nonlinear system. To design the PI controller for the uncertain system, first, it is transformed into a state feedback design for an augmented uncertain system and then the state feedback gains satisfying some LQ performance limit are computed by solving a linear matrix inequality (LMI) problem. As the uncertainty in the feedforward matrix of the linearized model cannot be considered in the above design process, an LMI-based method is developed to check if the designed PI controller performance in H-infinity sense is close to the one if the neglected uncertainty is included. The performance of the controller is tested on the nonlinear boiler-turbine unit under several operating conditions and physical constraints. Comparisons are also made with some existing PI controllers, to show the superiority of the proposed robust PI controller.