An Efficient AsNMPC Implementation Based On Gauss Pseudospectral Method

With the development of computer hardware and software,researchers try to extend model predictive control(MPC)to fields involving fast dynamics such as automotive,aerospace,etc.However,an open-loop optimal control problem(OCP)is needed to be solved for the traditional MPC during each sampling interval.Due to the online high computational cost,the applications of MPC are mainly restricted in the field of process control with slow dynamics.Fast optimal control algorithm and efficient MPC computing framework are the key techniques to achieve this goal.Advanced step nonlinear MPC(asNMPC)reduces the time delay between obtaining state measurement and control feedback by the procedure of one-step prediction,computation of the optimal solution and sensitivity update.It requires solving an open-loop OCP during one sampling interval.This thesis attempts to accelerate the optimization procedure in asNMPC by using global Gauss pseudospectral,and to stabilize the closed-loop system by replacing finite horizon OCP with infinite horizon OCP in each sampling interval.Meanwhile,the software design is also simplified.The main works are as follows:(1)A Gauss pseudospectral is designed to solve the infinite horizon OCP for index-1 differential algebraic systems.The strictly monotone logarithmic function is used to transform infinite horizon to finite horizon,and discretize the OCP in the transformed horizon.This algorithm can avoid the singularity of numerical operation at infinity by excluding terminal nodes in integral and differential calculation.When the lower order pseudospectral discretization is used,the decision variables obtained by the proposed algorithm are less than those obtained by asNMPC with multi-interval Runge-Kutta.Moreover,there is no need to introduce the terminal constraint to ensure the closed-loop stability.The numerical simulation of Delta robot shows that the algorithm converges quickly with 5 Gauss nodes.(2)An asNMPC embedded with Gauss pseudospectral is designed and implemented where the algorithm divides the optimization problem into two parts:offline preparation and online calculation.In the offline preparation,the state of the next sample time is predicted based on the current state and control,and Gauss pseudospectral is used to solve the infinite horizon OCP.At the next sampling time,the NLP sensitivity is used to update control and once the measurement of the state is obtained.The algorithm is implemented based on the NLP solver Ipopt,and the sensitivity update is completed by sIPOPT.The simulation of Delta robot shows that the algorithm can effectively reduce the feedback delay,has strong robustness to the model mismatch,and the computational speed increases rapidly with the decrease of discretization order.