Control design for a class of unstable nonlinear systems with input constraint

The motion control subjects explored in this dissertation include linearization of a nonlinear system about an equilibrium manifold, recovering the stability of an unstable plant from control saturation, transition control among operating points with distinct system characteristics, and performance improvement of repetitive motion via iterative learning control. The research conducted here is mainly inspired by the study of a hydraulically balanced beam control system, which is an open-loop unstable nonlinear system with a connected set of equilibrium points and input constraint. Based on the system characteristics and the intended motion, several interesting new ideas on the control design are proposed to complement existing methodologies.; In a manner conceptually similar to the Jacobian linearization, the nonlinear control system with a connected set of equilibrium points can be approximately linearized about the equilibrium manifold by prescribing the control reference along the equilibrium manifold direction. In contrast to feedback linearization, this method is still valid for non-minimum phase nonlinear systems, i.e. systems with unstable internal dynamics, if their internal and external subsystems are interconnected by the equation of equilibrium manifold.; Input saturation, a very common nonlinearity in mechanical control systems, may be incurred by exogenous disturbances and infeasible trajectory planning. It can not only deteriorate the system performance but also destroy the stability of an open-loop unstable system. A “soft” tracking strategy is proposed here which relaxes the requirement of desired trajectory to reduce the saturation extent and thus preserve the system stability. The soft reference is constructed on-line by infusing the system dynamics into the desired trajectory to provide a feasible path for the system to recover from input saturation and then return to the original desired motion.; Controlling the transition from a stable resting to tracking control of a open-loop unstable system is nontrivial and challenging. Due to the unavailability of system initial motion conditions, feasible trajectory planning is unlikely to be possible beforehand. On the other hand, the exogenous disturbance and measurement noise contribute to the difficulty in defining transition condition for the finite state machine. With the help of the soft tracking strategy and fuzzy decision making, these two categories of difficulty can be resolved and the transition can be smoothly executed.; Once the stability of system has been secured, performance is the next control goal. For systems with repetitive motion, iterative learning control can be employed to improve the performance by learning appropriate control action from previous trials. Integral learning is the simplest point-wise learning method, while the neural network is a universal function approximation tool. With the cooperation of integral learning and neural learning of inverse system dynamics, the learning capability can be significantly improved for most mechanical systems. However, for systems with reverse control effort between tracking and stabilization, the learning of system inverse dynamics is unlikely to improve the tracking performance. By learning the previous value of integral learning instead, the neural network may learn the relationship between tracking effort and the system output, and thus improve the learning capability.; All of the control techniques proposed here have been successfully verified through the real-time implementation in the balance beam control system. The underlying design ideas can be further applied to the control design of general systems.