Using normalized simultaneous perturbation stochastic approximation for stable convergence in model-free control scheme

This paper presents a normalized SPSA for stable convergence in model-free control scheme. Initially, an unstable convergence of conventional SPSA is illustrated, which motivate us to introduce its improved version. Here, the conventional SPSA is modified by introducing a normalized gradient approximation to update the design variable. To be more specific, each measurement of the objective function from the perturbations is normalized to the maximum objective function measurement at the current iteration. As a result, this improvement is expected to avoid the updated control parameter from producing an unstable control performance. The effectiveness of the normalized SPSA is tested to model-free PID control scheme of liquid slosh system. The simulation results are presented in terms of the convergence responses and control performances. The outcome of this paper shows that the model-free controller tuning using the normalized SPSA is able to provide stable and better control performances as compared to the existing modified SPSA.