Model Updating Strategy
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. If you have reliable and simple symbolic equations for your plant model, you might be able to derive, offline, a symbolic expression of the linearized plant matrices at any given operating condition. Online, you can then calculate these matrices and supply them to the adaptive MPC controller without having to perform a numerical linearization at each time step. For an example using this strategy, see Adaptive MPC Control of Nonlinear Chemical Reactor Using Successive Linearization.
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. For an example using this strategy, see Adaptive MPC Control of Nonlinear Chemical Reactor Using Linear Parameter-Varying System.
Online parameter estimation — Given a stable plant having a known empirical model structure with initial estimates of its parameters, and where a minimal amount of noise guarantees some persistence of excitation, you can use the available real-time plant measurements to estimate the current model parameters. Since online estimation can be more computationally intensive than interpolation or direct model update from the scheduling variables, in general this method is reserved for control applications where longer control intervals and good computational resources are available. For example, the System Identification Toolbox™ software provides real-time parameter estimation tools. For an example using this strategy, see Adaptive MPC Control of Nonlinear Chemical Reactor Using Online Model Estimation.
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 to obtain the plant model from the scheduling variables, ahead of time, at each operating condition along the expected trajectory.
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 especially if online parameter estimation is required.
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.Plantproperty of the controller. The disturbance and noise models, if any, remain constant.