Model Predictive Control 2 - Generalised predictive control and dynamic matrix control

Introduces the concept of an 'independent model'. Shows how this differs from more conventional prediction models and the impact this has on the construction of the control law. Backed up with MATLAB code and demonstrations.

Uses MATLAB to illustrate code required to do GPC with a T-filter and compare behaviour with and without a T-filter. Considers prediction, control law formulation, simulation and sensitivity. Code is all available on the googlesites.

Introduces the T-filter. What is it and why is it included? How is it included and how does this affect the predictions to be deployed in a GPC control law.

Uses the context of GPC in the earlier videos to introduce DMC and thus highlight the main conceptual similarities and differences.

How does the T-filter change behaviour. Derives the GPC law with predictions based on a T-filter and then looks the changes to the closed-loop transferences and sensitivity with a T-filter and shows how these compare to GPC without a T-filter.

Looks at how the GPC control law changes if one wants to use a state space model. For convenience, proposes a slightly different choice of performance index. Also demonstrates the equivalent state feedback and hence how once could determine closed-loop poles.

Demonstrates some simple MATLAB code for developing and implementing a GPC control law, SISO and MIMO case. Code is highly transparent but also simple so that users can edit easily, modify horizons, weights, models and overlay responses for different choices. Code available on the googlesites.

Demonstrates how the closed-loop control law parameters and associated pole polynomial can be computed for the SISO and MIMO cases. Illustrates simple (easy to edit) MATLAB code available for students to do their own examples.

Shows how one can combine the predictions and a performance index in order to form a GPC control law. Includes an aside on optimisation of multivariable functions. The law is given in matrix/vector format and shown to be linear in the core signals (target, input and output).

Looks at logical prediction structures for predictive control and the degrees of freedom within these. Also demonstrates how one can form compact representations of performance indices which enable simple matrix/vector algebra and optimisation.

Shows how the GPC control law expressed in matrix/vector format can be interpreted as being equivalent to a transfer function implementation. Gives the associated closed-loop block diagram and the details required to form the control law parameters.

Introduces the sensitivity functions for a simple GPC feedback loop. Demonstrates through examples that although disturbance rejection is good, noise rejection may be very poor and indeed could be considered unsatisfactory.