ANALYSIS AND DESIGN LINEAR MODEL PREDICITIVE CONTROL WITH MATRIX INEQUALITIES

• Main Author: GANESHA SRI BAGUS WARMAN (NIM 23205028), ESHA
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/7837
• Institution: Institut Teknologi Bandung

Model Predictive Control (MPC), also known as receding horizon control, is the most effective tools deal with multivariable constrained control problem. The constraint can be system constraints, input and output constraints. Main principle of MPC is finding optimal input sequence by online optimization of objective function with horizon to predict future system behavior. Only first of optimal input control will be given to the plants. MPC Implementation issues are stability closed loop and performance of MPC <br /> <br /> <br /> Stability and performance MPC is influenced by some parameters in objective function. Optimization of objective function is using Quadratic Programming (QP) algorithm. There is equivalence between algebraic loop nonlinear and QP, so there is alternative implementation of MPC, both regulator and tracking MPC problem. That implementation can be considered as Lure’s problem for stability analysis. Stability analysis of Lure’s problem will get a sufficient condition of matrix inequalities for MPC stability analysis and design. A sufficient condition of matrix inequalities to find some parameters in objective function for MPC stability analysis and MPC design may be possible. <br /> <br /> <br /> A sufficient condition of Bilinear Matrix Inequalities (BMI) is used for MPC stability analysis solving feasible solution of BMI by iteration process, although these method is not guarantee convergen. Weight matrices of MPC that is found from solution of BMI for stability analysis may be also possible. MPC implementation with those matrices will be guarante stable. <br /> <br /> <br /> MPC design formulation based on performance criteria l2-gain is found as a sufficient condition of BMI. Solving minimization l2-gain of BMI by iteration process. Some parameters MPC design based on performance criteria l2-gain may be possible by BMI. <br /> <br /> <br /> Simulation examples for stability analysis using matrix inequalities are given. Plants for simulation example for stability are double integrator dan TITO. Simulation example plant for MPC design is TITO plant. MPC design example is given in two methods, i.e BMI and Linear Matrix Inequalities (LMI). <br /> <br /> <br /> Stability test may be done by solving LMI. Simulation examples have been shown that converting LMI to BMI, some MPC parameters may be searched by iterative process with a stability guarantee. <br /> <br /> <br /> Solving BMI by iterative process is not succeed yet. But, using less strict convergen criteria, iteration process may be found for some cases. System response using that iteration process have shown a sufficient MPC response. System response from MPC design based on performance criteria l2-gain is not satisfied. Simulation examples have shown that MPC performace can not be possible using l2-gain criteria. <br /> <br /> <br /> Using other performance criteria for finding MPC design formulation with matrix inequalities may be done for next research. <br />