Application Of ADMM To Model Predictive Control Problems For A Class Of Turbofan Engine

This article studies the model predictive control(MPC)problem of a class of linear time invariant(LTI)systems.The LTI system is based on turbofan aeroengines.Firstly,we use ADMM to study the MPC problem of turbofan engines based on the LTI model.We first derive the predictive equations at the current moment k based on the LTI model and the basic principles of MPC.Secondly,we use the predictive equations to transform the MPC problem into a quadratic programming(QP)problem about the control sequence and then introduce a slack variable to convert the QP problem into a block optimization problem with equality constraints which is suitable for ADMM framework.Finally,the ADMM is used to complete the subsequent solving process to obtain the optimal control sequence.Based on this,we propose an improved MPC-ADMM algorithm and compare the algorithm with the traditional QP algorithm through numerical examples.The experimental results show a faster response obtained the ADMM to the fan speed within allowable limits of the control and output.Moreover,when the control horizon and prediction horizon are longer,the CPU consumption time of the ADMM is shorter which shows that the proposed optimization algorithm is effective and superior.Secondly,we use the ADMM to study the robust model predictive control(RMPC)problem which is a min-max optimal problem based on the LTI model with external interference on the basis of the above MPC problem.We use the optimality conditions of the original optimization control problem(OCP)to transform the OCP into a variational inequality(LVI)problem at the current moment k and use the proximal point algorithm(PPA)to transform the LVI problem into two QP problems.We finally use ADMM to complete the subsequent solving process.Based on this,we propose an improved RMPC-ADMM algorithm and compare the algorithm with the MPC-ADMM algorithm through a numerical example to show that the RMPC-ADMM algorithm is effective—it has a certain degree of robustness.In addition,we compare the simulation results of ADMM and QP algorithm to illustrate the superiority of the RMPC-ADMM algorithm which is that the CPU consumption time of this algorithm is also shorter in the case of external interference for the same RMPC problem mentioned above.