Smith predictor

Process Control A Practical Approach Myke King 2011 John Wiley Sons Ltd. ISBN 978-0-470-97587-9 

The trend for the control PV shows a typical transient disturbance immediately the process deadtime has elapsed. This comes from the corrector and is caused by a mismatch between the actual and the predicted PV. It might arise because of a difference between the process deadtime and the deadtime in the plant model. It might also be caused by the plant model being hrst order plus deadtime whereas the process probably has a higher order. It is this transient that can limit how large a gain may be used in the PID controller. The controller will respond to it as if it is a load disturbance and the action it takes will later, when the deadtime has elapsed, cause a disturbance in the actual PV. This will then repeat at 

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The Smith predictor is a model-based control strategy that involves a more complicated block diagram than that for a conventional feedback controller, although a PID controller is still central to the control strategy (see Fig. 8-37). The key concept is based on better coordination of the timing of manipulated variable action. The loop configuration takes into account the facd that the current controlled variable measurement is not a result of the current manipulated variable action, but the value taken 0 time units earlier. Time-delay compensation can yield excellent performance however, if the process model parameters change (especially the time delay), the Smith predictor performance will deteriorate and is not recommended unless other precautions are taken. 

FIG. 8-37 Block diagram of the Smith predictor. The process model used in the controller is G = G°e (G = model without delay = time delay element). 

Apply classical controller analysis to cascade control, feedforward control, feedforward-feedback control, ratio control, and the Smith predictor for time delay compensation. 

There are different schemes to handle systems with a large dead time. One of them is the Smith predictor. It is not the most effective technique, but it provides a good thought process. 

The time delay effect is canceled out, and this equation at the summing point is equivalent to a system without dead time (where the forward path is C = GCGE). With simple block diagram algebra, we can also show that the closed-loop characteristic polynomial with the Smith predictor... 

In a chemical plant, time delay is usually a result of transport lag in pipe flow. If the flow rate is fairly constant, the use of the Smith predictor is acceptable. If the flow rate varies for whatever reasons, this compensation method will not be effective. 

The Smith Predictor for deadtime compensation is a feedback controller that has... 

There is a special type of controller, called a Smith predictor or deadtime compensator, that can be applied in either continuous or discrete form. It is basically a special type of model-based controller, in the same family as IMC. Figure 20.6a gives a sketch of a conventional feedback control system. Let s break up the total openloop process into the portion without any deadtime G j,(s) nd deadtime e... 

But if the Smith predictor (sketched in Fig. 20.6b) is used, the closedloop characteristic equation is changed. First, let s consider the inside feedback loop. The closedloop relationship between M and E is... 

In theory, the Smith predictor gives significant improvement in control. In practice, only modest improvement can be achieved in many processes. This is due to the sensitivity of the stability of the system to small changes in system parameters. If the controller is tightly tuned and there is a small shift in the actual deadtime of the process, the system can go unstable. Therefore, most of the successful applications have been in processes which have gains, time constants, and deadtimes that are well known and constant. Examples include paper machines, steel rolling mills, and textile manufacturing. 

Brosilow, C.B. The Structure and Design of Smith Predictors from the Viewpoint of Inferential Control (1979) Joint Automatic Control Conference, Denver... 

The presence of significant amounts of dead time in a control loop can cause severe degradation of the control action due to the additional phase lag that it contributes (see Example 7.7). One method for compensating for the effects of dead time in the control loop has been suggested by SMITH<30>. This consists of the insertion of an additional element which is often termed the Smith predictor as it attempts to predict the delayed effect that the manipulated variable will have upon the process output. 

It can be seen from equation 7.144 that implementation of the Smith predictor assumes knowledge of the transfer functions (i.e. the dynamics) of the process (including the dead time) and the final control element. These are unlikely to be... 

To improve the performance of time-delay systems, special control algorithms have been developed to provide time-delay compensation. The Smith predictor technique is the best-known algorithm a related method is called the analytical predictor. Various investigators have... 

FIG. 8 38 Block diagram of the Smith predictor. (Source Seborg et al., Process Dynamics and Control, 2d ed., Wiley, New York, 2004.)... 

As shown in part (b) of Figure 2.85, the Smith-predictor compensator provides a process model in terms of its time constant and dead time and thereby predicts what the analyzer measurement should be between analysis updates. When an actual analysis is completed, the model s prediction is compared... 

Once a process model has been established, it is possible to build the inverse of that model, which can be used as a controller. A simple internal model-based controller (IMC) is the Smith-predictor (Figure 2.85b), which is a first-order system with dead time combined with a PI controller. 

This design may yield controllers which are quite sensitive to model errors and require high order derivative action. If the dead time in P(s) is the same as the dead time in G(s), the controller contains dead time compensation, as in the Smith predictor. Bristol (42) has extended this idea to apply to multivariable systems, although he treats the controller in a more general form, allowing a pre-compensation block before G(s) and a postcompensation block after G(s) in the direct path between r(s) and y(s). 

As shown in the above works, an optimal feedback/feedforward controller can be derived as an analytical function of the numerator and denominator polynomials of Gp(B) and Gn(B). No iteration or integration is required to generate the feedback law, as a consequence of the one step ahead criterion. Shinnar and Palmor (52) have also clearly demonstrated how dead time compensation (discrete time Smith predictor) arises naturally out of the minimum variance controller. These minimum variance techniques can also be extended to multi-variable systems, as shown by MacGregor (51). 

In Section 19.2 we discussed how we can develop a Smith predictor (dead-time compensator) which cancels the effect of dead time. The same general concept of the predictor (compensator) can be used to cope with the inverse response of a process and was proposed by Iinoya and Altpeter [Ref. 5]. 

Adding the signal y (s) to the main feedback signal y(s) means the creation of the local loop around the controller as shown in Figure 19.5b. The system in this local loop is the modified Smith predictor and the actual compensator of the inverse response. As can be seen from eq. (19.6), its transfer function is... 

In the preceding section we identified the critical need for more effective control of processes with significant dead time. In this section we discuss a modification of the classical feedback control system which was proposed by O. J. M. Smith for the compensation of dead-time effects. It is known as the Smith predictor or the dead-time compensator. 

The dead-time compensator predicts the delayed effect that the manipulated variable will have on the process output. This prediction led to the term Smith predictor and it is possible only if we have a model for the dynamics of the process (transfer function, dead time). 

In most process control problems the model of the process is not perfectly known that is, G(s) and td are known only approximately. Consider that G(s) and td represent the true characteristics of the process, while G (s) and td represent their approximations, as these are given by some mathematical model for the process. Then, using G (s) and t d to construct the Smith predictor, we take the system shown in Figure 19.3. In this case the composite open-loop feedback signal is... 

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