Model Predictive Heuristic Control

Early applications of MPC took place in the 1970s, mainly in industrial contexts, but only later MPC became a research topic. One of the first solid theoretic formulations of MPC is due to Richalet et al. [53], who proposed the so-called Model Predictive Heuristic Control (MPHC). MPHC uses a linear model, based on the impulse response and, in the presence of constraints, computes the process input via a heuristic iterative algorithm. In [23], the Dynamic Matrix Control (DMC) was introduced, which had a wide success in chemical process control both impulse and step models are used in DMC, while the process is described via a matrix of constant coefficients. In later formulations of DMC, constraints have been included in the optimization problem. Starting from the late 1980s, MPC algorithms using state-space models have been developed [38, 43], In parallel, Clarke et al. used transfer functions to formulate the so-called Generalized Predictive Control (GPC) [19-21] that turned out to be very popular in chemical process control. In the last two decades, a number of nonlinear MPC techniques has been developed [34,46, 57],... 

J. Richalet, A. Rault, J.L. Testud, and J. Papon. Model predictive heuristic control application to industrial processes. Automatica, 14 413-428, 1978. 

Model Predictive Heuristic Control Applications to Industrial Processes," Automatica, 1978, 14, 413. 

Richalet, J. A., Rault, A. Testud, J. D., and Papon, J., Model predictive heuristic control Application to industrial processes, Automatica 13, 413 (1978). 

Richalet J, Rault A, Testud JL, Papon, J. Model predictive heuristic control - apphcahons to industrial processes. Automatica 1978 14 413-428. 

The second level is the advanced and predictive control. These are two different control schemes that work at the same level. Information is transmitted horizontally and vertically in this (and upper) level. More elaborated control strategies as selective control, ratio control, feedforward control are implemented. In this second level implicit as well as explicit (heuristic and first principles based) models are used to generate the action. The action is the set point (goal) to achieve at the lowest level. Prediction horizon is (in the case of model predictive control) of tens of movements. 

Since biological processes are generally very complicated, they have not been fully described using mathematical models. However, hybrid process modeling based on all the available knowledge and information provided by means of mathematical models, heuristic knowledge or even by data sets has been shown to be useful for process state estimation, prediction and control [50, 51]. 

Regulatory control node. This is the simplest node. It implements the simplest RCS node, one in which the behavior is purely reactive. It has a World model (the PID algorithm is a model, an empirical or heuristic model, but a model of the system under control), but this model does not predict the behavior. It only reacts to the current values of the plant and decides an action to be performed (there is no plan, it is just an action for the next time). It can be considered to have a KD where the model parameters are stored. Very simple preprocessing is performed (but some it is done as signal failure,...)... 

To interpret the formation of a periodic pattern we need to consider the displacement of material and to identify the physical origin of periodic phenomena. From the point of view the fact that the tip velocity and applied load control the amplitude of the period must help. The following simple model might give a useful, heuristic approach that should help to predict results for further experiments. 

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