Performance study of disturbance rejection in linear quadratic controllers: A practical adaptive tuning method

This paper proposes an adaptive tuning method for the Linear -Quadratic FeedForward (LQ-FF) optimal controller. The procedure aims to reject disturbances while maintaining the reference tracking performance of the conventional LQ controller. The adaptive mechanism is formulated by analyzing each element of the control signal LQ-FF concerning state regulation, reference change, and disturbance compensation. The disturbance rejection mechanism is based on the classical strategy used in Proportional -IntegralDerivative controllers and the theoretical analysis studied in previous works for predictive controllers, which aim to obtain the inverse dynamics of the disturbances and process inputs in relation to the outputs. In addition, a comparison is presented between an augmented state space model and a model with a polynomial delay approximation for treating delays associated with disturbances and process inputs in the controller formulation. The proposed method effectively controls a validated nonlinear temperature system, maintaining performance equivalent to the conventional LQ controller for reference tracking while entirely rejecting disturbance effects. The proposed tuning achieves 10 % less output error, with an increase of only 18 % in the control effort compared to conventional tuning in simulations.