Algorithm Study On Input Constrained Model Predictive Control

In real control systems there may be various constraints present. These constraints can begenerally categorized as control constraints and state constraints.The controller servers as the driving force in the overall control system and a goodcontrol strategy can stabilize an otherwise unstable system while fulfilling the stateconstraints. Model Predictive Control is such control strategy. However, when the systemconstraints are satisfied, the controller may have already violated input constraints. Thestability, state constraints and performance of the system cannot be guaranteed if the inputsdon’t stay within the input constraints.Also, when the predictive control algorithm is appliedto fast sampling systems, there is great demand on the controller’s computing speed. And thefulfillment of the input constraints complicates the problem.In this thesis, we give an analysis on the input constrained predictive control problembefore laying out the customized algorithms which have relatively low on-line computationalload while satisfying the input constraints.Firstly, we described in detail the structure of a predictive controller and gave the matrixrepresentation of the optimization problem used in the online quadratic programmingprocedure. We also described the dual-mode predictive control paradigm which guarantees theoptimality of the cost function. Based on this paradigm we gave the algorithm for dual-modelinear quadratic model predictive control.Secondly, specific analysis was given to stability and feasibility of the input constrainedmodel predictive control problem. The maximum terminal target set is an important conceptto guarantee stability of the system. We therefore give the algorithm for calculating themaximum target set. Next we introduced the ellipsoid invariant target set. It reduces thecomplexity compared with the polyhedral target set.We then studied hyperbola input constraints. The variable horizon searching algorithmthat we proposed preserved the original structure of the optimization problem. And at eachsample instant, the horizon length was determined using the Fibonacci sequence. It reducesthe complexity which would otherwise be induced by the on-line sub-optimization problemfor find the suitable horizon. We proved the stability and feasibility of the proposed algorithm.The simulation that followed confirmed the effectiveness of the algorithm.Finally, we provided the Perturbation based Model Predictive Control algorithm. It hasmade improvements on both the optimization problem in the predictive control problem andthe structure of the terminal invariant target set. We run the simulation on the cantilever beammodel in which comparisons were made between the PMPC and common dual-mode modelpredictive control algorithms. The result showed that the PMPC algorithm effectively reducedthe on-line computation time while guaranteeing the stability and feasibility of the system.