A Tuning Strategy for Unconstrained Multivariable Model Predictive Control

Abstract

Move suppression coefficients serve a dual purpose in the model predictive controller (MPC) architecture. These include suppressing aggressive control action and conditioning the system matrix prior to inversion. The work presented here exploits this dual effect in deriving an analytical expression that computes appropriate move suppression coefficients as a function of process model parameters, other MPC design parameters, and partitioned block condition numbers of the system matrix. The development is based upon an approximate mosaic Hankel matrix structure of the multivariable system matrix. The primary contribution of this work is the derivation of the analytical expression for computing move suppression coefficients and its demonstration in an overall MPC tuning strategy (Table ). The examples presented show that the move suppression coefficient remains properly scaled as the other MPC design parameters and process characteristics change to produce a consistent closed loop performance. This tuning method is applicable to unconstrained multivariable processes, including non-square systems.

GOBF-ARMA based model predictive control for an ideal reactive distillation column

“…(28). The prioritizing of outputs robustness and speed adjustments can be done by adjusting the weighting matrices Q and R, respectively (Shah and Engell, 2011;Shridhar and Cooper, 1998). …”

Optimizing Model Base Predictive Control for Combustion Boiler Process at High Model Uncertainty

“…Georgiou et al 12 proposed setting the model horizon larger than the time required for the slowest open-loop process output response to reach 95 % of the steady state. Shridhar and Cooper 13 , and Wojsznis et al 14 proposed setting the model horizon equal to the final prediction horizon.…”

An analytical tuning approach to multivariable model predictive controllers

“…However, the multivariable MPC tuning problem is considered in few articles. In addition, the available multivariable MPC tuning strategies are based on numerical methods or experimental and practical guidelines and there is only one analytical approach which gives closed form tuning equations [10]. In [10], an analytical tuning method is given for multivariable dynamic matrix control (DMC) parameters based on the multivariable FOPDT model approximation of the plant.…”

“…In addition, the available multivariable MPC tuning strategies are based on numerical methods or experimental and practical guidelines and there is only one analytical approach which gives closed form tuning equations [10]. In [10], an analytical tuning method is given for multivariable dynamic matrix control (DMC) parameters based on the multivariable FOPDT model approximation of the plant. The control effort weight matrix tuning is considered to avoid singularity in the control signal calculation, however closed loop performance is not considered.…”