New control design and analysis techniques for plants with actuator nonlinearities

Actuator saturation is ubiquitous in physical plants. In closed-loop systems limits imposed on the actuators may result in degraded performance of the control law and, ultimately, instability of the system. When other non-linearities, such as deadzone, backlash or stiction, are also present in a system’s input, the analysis and design procedures become more involved. The core of this thesis is a new structure based on the right inverse approach for deadzone and backlash, which is extended to linear plants that exhibit a combination of saturation and either deadzone, backlash or stiction, in the actuator. It is shown that, for this type of system, the inclusion of the right inverse nonlinearity results in the linear plant being subject to a new input saturation. Then, one can design standard controllers such as anti-windup or input constrained MPC around this saturation. This simplifies the analysis and design processes, in spite of the presence of complex nonlinearities. The results for deadzone and backlash are extended to stiction by proposing an approximate stiction nonlinearity, and then introducing a right inverse to this approximation. It is demonstrated that the systems studied can be compensated by a standard input constrained MPC which can be solved by a convex quadratic program. Additionally, a simple anti-windup structure is used to demonstrate the applicability of the proposed structure using existing control strategies.