Typically, to implement Adaptive MPC control, you can use one of the following model-updating strategies:
Successive linearization — Given a mechanistic plant model, for example a set of nonlinear ordinary differential and algebraic equations, derive its LTI approximation at the current operating condition. For example, Simulink® Control Design™ software provides linearization tools for this purpose.
Using a Linear Parameter Varying (LPV) model — Control System Toolbox™ software provides a LPV System Simulink block that allows you to specify an array of LTI models with scheduling parameters. You can perform batch linearization offline to obtain an array of plant models at the desired operating points and then use them in the LPV System block to provide model updating to the Adaptive MPC Controller Simulink block.
Online parameter estimation — Given an empirical model structure and initial estimates of its parameters, use the available real-time plant measurements to estimate the current model parameters. For example, the System Identification Toolbox™ software provides real-time parameter estimation tools.
To implement Time-Varying MPC control, you need to obtain LTI plants for the future prediction horizon steps. In this case, you can use the successive linearization and LPV model approaches as long as each model is a function of time
There are several factors to keep in mind when designing and implementing an adaptive MPC controller.
Before attempting adaptive MPC, define and tune an MPC controller for the most typical (nominal) operating condition. Make sure the system can tolerate some prediction error. Test this tolerance via simulations in which the MPC prediction model differs from the plant. See MPC Design.
An adaptive MPC controller requires more real-time computations than traditional MPC. In addition to the state estimation calculation, you must also implement and test a model-updating strategy, which might be computationally intensive.
You must determine MPC tuning constants that provide robust performance over the expected range of model parameters. See Tune Weights.
Model updating via online parameter estimation is most effective when parameter variations occur gradually.
When implementing adaptive MPC control, adapt only parameters defining the
Model.Plant property of the controller. The
disturbance and noise models, if any, remain constant.