Abstract:The Laguerre series is a kind of orthogonal series in L2 space, which has good function approximation ability. It is currently used in the field of automatic control for continuous dynamic process modeling and digital controller design. In order to expand the application range of Laguerre series in continuous controller design, the type 0 Laguerre series transfer function model is improved to the type 1 quasi-Laguerre series transfer function model in this paper, and a quasi-Laguerre series controller with integral behavior is proposed. Subsequently the frequency domain characteristics of the quasi-Laguerre controller and the PID controller commonly used in industry are studied comparably. By expanding the quasi-Laguerre control system model and the desired model using the Maclaurin series, the tuning formula of the parameters of the pseudo-Laguerre controller is given. In the simulation experiments on three types of controlled plants, the system approximation performance and disturbance-objection performance of the quasi-Laguerre controller and the PID controller are compared. The results show that the quasi-Laguerre controller with a third-order expansion term outperforms the PID controller on both the system approximation performance and disturbance-objection performance. This will lead to a good application prospect for the proposed controller.
