ChE 433 DPCL Model Based Control Smith Predictors

Model Based Control What can we do with a process model? Improve performance. 3 Methods Internal Model Control Model Free Adaptive Control Model based PID controllers

Internal Model Control Dynamic Matrix Control, DMC, forward projection of a process change is placed in an array and output changes are based on a least error squared value of the projected process variable. Multivariable handout Minimal Prototype Controller, where the controller output change is based on a projected change in process variable. This algorithm does not even use any elements from a conventional PID algorithm.

Model Free Adaptive Control Uses neural network to control the process. The output will move the process variable to the set point based on an internal network, not determined by the user. Some “reasonable” understanding of the process dynamics required. The process dynamics can change and the algorithm will learn the new conditions without being told to retrain itself.

MBC, Model Based Control Introduced to improve control response with dominant dead time processes Smith Predictor Concept: If we know the process transfer function, we can place the transfer function in the feedback path and cancel the dead time effect.

Smith Predictor Smith Predictor describe how a “model” of the process is placed in the feed back path. The user believes that an exact calculation and representation is required to implement the technique. Consider the elements in the feedback path as compensation elements.

MBC Implementation The process model is divided into two sections, one that models the process first order time constants and a second that models the process dead time. The value of these terms are not precisely equal to the process model.

MBC Implementation The controller’s compensated dead time should be smaller that the process dead time and the time constants should be slightly longer than the largest time constant. The compensated dead time approx. 25 percent shorter than the process dead time and the compensated lag 25 percent longer than the process time constants.

MBC Implementation It is not necessary for these compensating elements be precisely defined. The estimated values are usually sufficient. ~ 85% It is not necessary to know the exact process gain It is not necessary to have linear behavior; the algorithm is configured to compensate for the model error.

MBC Implementation A “standard” PID algorithm with a remote set point, CAS_IN, can be used if the model compensating terms can be implemented in a separating computing function block external to the controller. Without an offset between set point and the algorithm output, and to correct for modeling error, a model correction term, MC is the ratio of the actual process variable to the output of the total process model, W. Model correction method should be implemented in any advanced model based control system

Feed Forward to MBC The disturbance test was done without implementing any feed forward. Feed forward be implemented external to the predicted algorithm. Difficult to suppress the compensating action based on the feed forward signal, move the valve some amount and not allow the compensating algorithm to adjust for the change. The algorithm will correct for model errors as designed.

Potential Problems If dead time and time constants change significantly, the control loop will operate with choppy behaviour and not stabilize Non–linearity can be compensated

Integral Delay Dead Time Compensation Add a delay before the integral function. Change in the error results in immediate change in the proportional action, reset or integral behavior will be delayed. Integral delay time should be equal to the process dead time. This prevents excessive integral action.

Problems Implementing Integral Delay Most commercially available controllers don't allow the user to configure the controller’s internal elements. DeltaV does not. LabView does. Many do not offer delay or dead time function blocks. A requires the controller manufacture to use more dynamic memory, which increases the cost Use multiple first orders to simulate a dead time