Hi All of u
I build a controller on the basics of model predictive contro (MPC),
i used a predictor then enter the predicted value and the deviation from its previous predicted value to the FLC to determine the necessary control action, is that a MPC or not?
if it is, where is the cost function that is minimized
In my opinion the controller that you describe is not a model-based predictive controller (MBPC). The predictive controller makes use of a process model to determine the optimal sequence of control actions. Those are obtained by minimizing a certain objective function.
Two points determine, however, the application of this methodology to nonlinear systems:
- It is required the availability of a model that can predict the outputs of a process in an extended control horizon with sufficient precision.
- In the case of a nonlinear model at each sampling instant, it will have to be solved a nonlinear optimization problem, often non convex.
The prediction of future outputs of the process, in the prediction horizon Hp, is performed using a system model. The values of the predicted outputs y*_(k+i) for i = 1,. . . , Hp, depend on the state of the process at time k (conditioned by the history of previous inputs and outputs) and on the future inputs (i.e. future control signals) u (k+i) for i = 0, ..., Hp - 1. Normally the control signal is manipulated in a more restricted period of time horizon designated control horizon Hc, remaining constant after that.
The size of the control horizon has direct consequences on the complexity of the subsequent optimization problem: the future control signals will be calculated through the optimization of a cost function that describes the control objectives.
A possibility for the cost function could be the sum of the quadratic errors of the predicted values towards the reference value (during the prediction horizon).
Although usually the control horizon is larger than the pure delay of the system, the first of the calculated control signals is the only one that is applied to the plant. At the next sampling instant it is already available the output y(k + 1) and the prediction and optimization with the updated values can be resumed.
In my opinion in order to have the required MBPC you should implement a fuzzy logic PD controller (having as inputs the error towards reference and the change of error) extended with an optimization module to tune all or some of its parameters (e.g. rules or scaling factors) according to the mentioned cost function.
It is not MPC. MPC with FLC could be used for the control of nonlinear and non-stationary systems.
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