Move suppression

Equation (8-66) contains two types of design parameters that can also be used for tuning purposes. The move suppression factor 8 penalizes large control moves, while the weighting factors Wj allow the predicted errors to be weighed differently at each time step, if desired. 

The MPC control problem illustrated in Eqs. (8-66) to (8-71) contains a variety of design parameters model horizon N, prediction horizon p, control horizon m, weighting factors Wj, move suppression factor 6, the constraint limits Bj, Q, and Dj, and the sampling period At. Some of these parameters can be used to tune the MPC strategy, notably the move suppression faclor 6, but details remain largely proprietary. One commercial controller, Honeywell s RMPCT (Robust Multivariable Predictive Control Technology), provides default tuning parameters based on the dynamic process model and the model uncertainty. 

To minimize /, you balance the error between the setpoint and the predicted response against the size of the control moves. Equation 16.2 contains design parameters that can be used to tune the controller, that is, you vary the parameters until the desired shape of the response that tracks the setpoint trajectory is achieved (Seborg et al., 1989). The move suppression factor A penalizes large control moves, but the weighting factors wt allow the predicted errors to be weighted differently at each time step, if desired. Typically you select a value of m (number of control moves) that is smaller than the prediction horizon / , so the control variables are held constant over the remainder of the prediction horizon. 

Move suppression factor, shift in target value Load step change Time step... 

This optimization can be trivially transformed to linear programming. A step disturbance equal to -0.05 and a step setpoint change equal to 0.05 enter the closed loop at time k = Q. For move suppression coefficient values to = ti < 0.5, the resulting closed-loop response is shown in Fig. 9. The closed loop is clearly unstable. If the move suppression coefficients take values ro = ri > 0.5 (to penalize the move suppression coefficients even more) the closed loop remains unstable, as shown in the Fig. 10. The instability is due to the nonminimum phase characteristics of the process. Although a longer optimization horizon length, p, might easily solve the... 

End condition, Eq. (79) Input move suppression coefficients Closed-loop behavior... 

For this MFC system, Eqs. (118) through (125), Vuthandam et al. (1995) developed sufficient conditions for robust stability with zero offset. These conditions can be used directly for calculation of minimum values for the prediction and control horizon lengths, p and m, respectively, as well as for the move suppression coefficients rji, which are not equal over the... 

Note that the inequality in Eq. (138) implies that weights of the input move suppression term containing Am gradually increase. Details can be found in Vuthandam et al. (1995) and Genceli (1993). A similar result can be found in Genceli and Nikolaou (1993) for MFC with /i-norm based online objective. Variations for various MFC formulations have also been presented. Zheng and Morari (1993) and Lee and Yu (1997) have pre-... 

The second class of dynamic tuning focuses on how much the MVs move for a given disturbance (either setpoint change or umneasured disturbance). This type of turfing parameter is commonly called move suppression and provides a mechanism to slow down some MVs relative to others. Move suppression is important when a given MV affects a critical piece of equipment, for example, a large compressor with many automatic overrides and shutdown interlocks. 

In the above equations (k + i) is a vector containing the values of the manipulated variables i hours ahead, NN(k + 0 is the RBF model prediction, E(k) is the current error between the actual output measurement and the model prediction and 9, R are the error and move suppression weights. 

An APC application responds quickly to process changes. A well-tuned model-predictive control application can run outside the comfort range of a human operator while pushing simultaneously against multiple process constraints. More significantly, a model-predictive control application can calculate moves for each MV every minute, which a plant operator cannot. Special techniques, such as move suppression, are used to prevent the plant from moving too far too fast. 

If a reference trajectory is employed, move suppression is not required, and thus R can be set equal to zero. 

The effect of a diagonal move suppression matrix R is apparent from a comparison of Cases B and D. 

The formulation of the new control strategy begins by introducing a general extended move suppression matrix IT of the form... 

The development of an extended predictive control for SISO and MIMO plants is presented. This work develops a new tuning strategy that is reliable for a broad class of SISO and MIMO processes and provides better performance than the move suppressed dynamic matrix controllers. The application of this strategy is demonstrated through practical real plant applications with good control performance. The EPC algorithm for SISO and MIMO plants provides a well-conditioned controller that is capable of fast closed-loop response. 

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