Design of LQR Tracking Controller Combined With Orthogonal Collocation State Planning for Process Optimal Control

Abstract

As one of the most important optimization methods for process optimal control, orthogonal collocation method has been widely used. However, this kind of optimization method is generally an open-loop optimization frame, which makes the model disturbances greatly affect the control performance and quality. In order to improve the optimal control performance of dynamic systems with disturbances, this work proposed an orthogonal collocation optimization-based linear quadratic regulator (OC-LQR) control method for process optimal control problems. Firstly, the orthogonal collocation method is derived in detail to transform the optimal control problem so that optimal state curves can be accordingly calculated. Then, an improved LQR controller design is proposed by using the obtained optimal state curves so as to construct the feedback control frame. On this basis, a state planning-based LQR tracking control is established with closed-loop control characteristics to tackle model disturbance problem. Meanwhile, the detailed Simulink model of the proposed control method is constructed for simulation execution. Finally, the proposed control structure is tested on a classical process optimal control problem with model disturbance (white noise) test and Gaussian mixture noise test to verify the performance of the proposed method. Simulation studies show that the control performance of the proposed method is excellent, where the mean absolute error of state curve tracking averagely reduces by 34.73% and the minimal performance index improves by 64.44% when compared with the classical orthogonal optimal control method. Simulation results demonstrate the effectiveness of the proposed planning-based tracking control framework.