Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Abstract

Abstract Feedforward control has been widely used to improve the tracking performance of precision motion systems. This paper develops a new data‐driven feedforward tuning approach associated with rational basis functions. The aim is to obtain the global optimum with optimal estimation accuracy. First, the instrumental variable is employed to ensure the unbiased estimation of the global optimum. Then, the optimal instrumental variable which leads to the highest estimation accuracy is derived, and a new refined instrumental variable method is exploited to estimate the optimal instrumental variable. Moreover, the estimation accuracy of the optimal parameter is further improved through the proposed parameter updating law. Simulations are conducted to test the parameter estimation accuracy of the proposed approach, and it is demonstrated that the global optimum is unbiasedly estimated with optimal parameter estimation accuracy in terms of variance with the proposed approach. Experiments are performed and the results validate the excellent performance of the proposed approach for varying tasks.

Keywords

• Optimisation techniques
• Simulation, modelling and identification
• Interpolation and function approximation (numerical analysis)
• Other topics in statistics
• Control system analysis and synthesis methods
• Self-adjusting control systems