Design and Analysis of Explicit Predictive Model Control to Reduce the Number of Convex Areas based on ParametricOptimization using Multi-Parameter Toolbox

In this paper, one of the challenges of predicting control based on the model is the implementation of explicitpredicting model control (EMPC) method in real time that EMPC provides an explicit and real time algorithm topredicting designed for implement explicit processes. When the predictive control is designed, the resulting costfunction is minimized. This cost function is a quadratic programming (QP) problem that has several forms. The generalstructure is that the cost function should be solved in relation to the optimization variable which is the control inputand minimize the optimal control signal of the cost function which is conditional on the initial state and system model.In this case, a convergent and optimal answer is obtained, in which case the control input implicitly depends on themode, i.e. the effect of the mode on the control input is undeniable, but it can’t be explicitly stated. The greater thenumber of system constraints, the longer the optimization problem will be solved, and if it varies over time, theexecution speed may be high or low. Therefore, numerical solution can’t be a real time method, i.e. it varies with thetime of the solution, this optimization problem is difficult to converge and optimize the answer. As a result, thecomplexity of the problem and the slowness of the solution are two problems that are encountered in online problemsolving. Especially to apply to explicit processes where control signals must be updated at all times. These two factorsgave rise to the EMPC, the practice of having system responses calculated offline in advance. According to theindependent variables that exist, a space is created that EMPC converts this space into convex regions and solves aMulti Parametric Toolbox (MPT) programming problem for each region and takes controllers and reduces the numberof convex areas.

Keywords:

Explicit Model Predictive Controller , Parametric Optimization , Convex Areas , Multi-Parameter Toolbox