LPV systems are linear systems whose dynamics depend on the scheduling parameter that can be measured online. For this reason, MPC for linear parameter varying (LPV) systems has been widely developed. Since an industrial process is inherently nonlinear to a certain extent, the control performance of linear MPC can deteriorate as operating conditions significantly change. Īn explicit linear model is typically used in the MPC formulation because the online optimization can be reduced to either a linear program or a quadratic program. Due to its ability to guarantee optimality while ensuring the satisfaction of constraints on input and state, MPC has received much interest in both industry and academia. Although an optimal control sequence is determined, only the first control action is applied to the plant.
At each sampling time, MPC solves a finite horizon optimal control problem based on an explicit model of the plant. Model predictive control (MPC), also known as receding horizon control, is an effective multivariable control algorithm in which a dynamic optimization problem is solved online. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance. The algorithm is illustrated with two examples. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws.
The online computational time is reduced by solving offline the linear matrix inequality (LMI) optimization problems to find the sequences of explicit state feedback control laws. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. Secondly, the piecewise optimizer is typically not convex, so a general PWA function is created instead (requiring 1 binary variable per region if the variable later actually is used in an optimization problem.An offline model predictive control (MPC) algorithm for linear parameter varying (LPV) systems is presented. To begin with, YALMIP searches for the Bi and Ci fields, but since we want to create a PWA function based on Fi and Gi fields, the field names have to be changed. To create a PWA function representing the optimizer, two things have to be changed. If the field Ai is non-empty (solution obtained from a multi-parametric QP), a corresponding PWQ function is created (pwq_yalmip.m). YALMIPs automatic convexity propagation fails), a MILP implementation is also available. In case the PWA function is used in a nonconvex fashion (i.e. The will exploit the fact that the PWA function is convex and implement an efficient epi-graph representation. The dedicated is implemented in the file pwa_yalmip.m. The pwf command will recognize the MPT solution structure and create a PWA function based on the fields Pn, Bi and Ci. Valuefunction = pwf ( sol, x, 'convex' ) To create a PWA value function after solving a multi-parametric LP, the following command is used. In principle, they are specialized objects. The first thing that might be a bit unusual to the advanced user is the piecewise functions that YALMIP returns in the fourth and fifth output from solvemp.
The reason is that the max operator applied to quadratic functions will generate quadratic constraints, which not is supported by the parametric solvers in MPT. Note that quadratic objective functions not can be used for dynamic programming with polytopic systems in YALMIP. Constraints = objective = 0 for k = N - 1 : - 1 : 1 % Feasible region constraints = [ constraints, - 1 = 0 ), implies ( d ) end