Nonlinear model predictive control system: Stability, robustness and real-time implementation

Model predictive control (MPC), also known as receding horizon control (RHC) is a feedback control scheme where a finite horizon open-loop optimization problem is solved on-line at each time instant with the current state as the initial state. Each optimization generates the optimal control trajectory. The resulting control trajectory is applied to the system until the next system measurement is available. MPC is particularly useful when the optimal feedback control law is difficult or impossible to implement. It has been traditionally applied to process control where slow system response allows time for the on-line optimal control computation.; A class of nonlinear model predictive control (NMPC) law based on gradient-based iteration is analyzed and implemented real-time in this thesis. This NMPC law takes only a finite number of Newton steps in each sampling period instead of solving the complete optimal control problem. The key attribute of the NMPC algorithm used here is that it only seeks to reduce the error at the end of the prediction horizon rather than tries to find the optimal solution. This reduces the computation load and allows for real-time implementation. The nominal stability is shown for a class of discrete-time control-affine system that the NMPC algorithm has some inherent robustness property with respect to external disturbances and modelling errors. This property follows from the exponential convergence of the predicted state error (i.e., terminal state error). It means that at least the predicted state error would remain bounded provided that the external disturbance and parameter variations are sufficiently small. Bounded state and measurement noise as well as gain variation are considered as the uncertainty model that the system can endure to maintain stability. The robustness of NMPC scheme is analyzed and quantified with the explicitly-defined uncertainties. This is also illustrated by simulation for a variety of nonlinear control-affine system.; In addition to simulation examples, the NMPC algorithm is also applied to the swing-up control experiment of a rotary inverted pendulum. The actuator constraint is incorporated via exterior penalty function. We also discuss the implementation strategy, state estimation issue, and experimental results. In addition to NMPC based swing-up control, we also present results from iterative learning control, using a similar algorithm.