Compensators Design using Laguerre Polynomials Applied to a Real Steer-by-Wire System of Autonomous Vehicle

This paper provides two main contributions to the field of control systems design. Firstly, an algorithm is proposed for computing digital compensators aimed at stabilizing a specific class of linear time-invariant discrete-time systems. The method leverages pole placement to devise a control system that uses a digital compensator within a closed-loop configuration. The poles crucial to this design are determined as roots of sequences of Schur polynomials, constructed via a linear combination of Laguerre polynomials orthogonal to a modified version of the classical Laguerre measure. This design yields an infinite family of compensators capable of stabilizing strictly proper plants by manipulating parameters within the coefficients of orthogonal polynomials. Secondly, the effectiveness of this approach is demonstrated through configuring a compensator for a real Steer-by-Wire platform using an industrial and embedded vehicle control unit with the CAN communication protocol. Additionally, experimental tests show improved performance compared to traditional tuning for PID controllers. The Error-to-Signal Ratio index is reduced by the novel algorithm by up to 35.5% and 65.6% in contrast with the PID controller against DLC and Fishhook procedures.