On the significance of the noise model for the performance of a linear MPC in closed-loop operation

Abstract

This paper discusses the significance of the noise model for the performance of a Model Predictive Controller when operating in closed-loop. The process model is parametrized as a continuous-time (CT) model and the relevant sampled-data filtering and control algorithms are developed. Using CT models typically means less parameters to identify. Systematic tuning of such controllers is discussed. Simulation studies are conducted for linear time-invariant systems showing that choosing a noise model of low order is beneficial for closed-loop performance.

A Riccati-Based Interior Point Method for Efficient Model Predictive Control of SISO Systems

“…While the latter paper dealt with filtering, prediction and tuning of the MPC-based control system for AP, here we delve into the detailed implementation of the controller. The reader may find it helpful to consult (Hagdrup et al, 2016) for further elaboration of the signal model used, the description of which will here by necessity be relatively brief.…”

“…The deterministic input u is subject to the Zero-Order-Hold condition (ZOH) while the discretization of stochastic part involves sampling a Stochastic Differential Equation (SDE) as described in (Hagdrup et al, 2016). The deterministic part of the system description may be realized as a state space model of the form…”

“…The Kalman Filter and Predictor result from the transfer functon H(s) as described in (Hagdrup et al, 2016).…”

“…As elaborated in (Hagdrup et al, 2016) the finite horizon optimal control problem (OCP) with objective function (5), subject to Kalman predictions for (1), input constraints (7) and soft output constraints (6) has an equivalent formulation in terms of the modified objective φ *…”

“…The relevant simulation parameters are listed in the tables below. The value for the weight ρ on the rate-of-input is arrived at by considering a Pareto-plot as in (Hagdrup et al, 2016). This is obtained by mapping integrated squared output error against integrated squared rate-ofinput for values of ρ ranging through a wide interval.…”