Equilibrium Drift Restriction: A Control Strategy for Reducing Steady-State Error Under System Inconsistency

The inconsistency of system parameters inevitably emerges due to reasons such as modeling imprecision, manufacturing error, and aging process. Due to the inconsistency between nominal models and real-world conditions, controllers designed accordingly frequently fail to maintain performance guarantees during physical deployment. This phenomenon exemplifies the open sim-to-real gap problem. To address this limitation, we develop an equilibrium drift restriction strategy (EDR) to reduce the steady-state error due to the system inconsistency. We first present an example to show the reason why some existing controllers cannot counteract the system inconsistency when the equilibrium is not at the origin. Then, a control strategy is proposed by using the EDR method to reduce the induced steady-state error. Both intuitive interpretation and theoretical analysis demonstrate how EDR reduces steady-state deviations. Simulation results of a common pendulum system are provided to demonstrate that the restriction mitigates the impact of parameter inconsistency. A comparison with the popular Q-learning method is also presented. The results show that the EDR method can serve as a simple but effective tool to improve the steady-state performance of existing controllers. This paper offers a fresh perspective for exploring the control functions with specific properties in the realm of related controller research.