Adaptive Quasi-Static Control of Multistable Systems

In some applications of control, the objective is to optimize the constant asymptotic response of the system by moving the state of the system from one forced equilibrium to another. Since suppression of the transient response is not the main objective, the feedback control law can operate quasistatically, that is, extremely slowly relative to the open-loop dynamics. Although integral control can be used to achieve the desired setpoint, three issues must be addressed, namely, non-linearity, uncertainty, and multistability, where multistability refers to the fact that multiple locally stable equilibria may exist for the same constant input. In fact, multistability is the mechanism underlying hysteresis. The present paper applies an adaptive digital PID controller to achieve quasi-static control of systems that are nonlinear, uncertain, and multistable. The approach is demonstrated on multistable systems involving unmodeled cubic and backlash nonlinearities.