Set point tracking

PI controllers are most common. They eliminate offsets and have acceptable speeds of response in most industrial settings. We usually pick a low to intermediate gain (wide proportional band, PB 150) to reduce the effect of noisy signals (from flow turbulence also why we do not use D control). We also use a low reset time ( 0.1 min/repeat i.e. relatively large I action) to get fast set-point tracking. 

In Eq. (10-5), 1/Gp is the set point tracking controller. This is what we need if we install only a feedforward controller, which in reality, we seldom do.4 Under most circumstances, the change in set point is handled by a feedback control loop, and we only need to implement the second term of (10-5). The transfer function -GL/Gp is the feedforward controller (or the disturbance rejection... 

The set point tracking controller not only becomes redundant as soon as we add feedback control, but it also unnecessarily ties the feedforward controller into the closed-loop characteristic equation. 

Fig. 6. (a) Set-point tracking performance of the TOC concentration when the RGA-AW is applied (S - dashed line, St, gray line and St- black line), (b) Dynamical response of the manipulated variable (black line Q calculated by the control law and gray line Q measured at the entrance of the digester). 

Whenever the secondary controller is in manual or on local set point, the status is communicated backward to the primary controller via the TCO-TCI communication link. At the same time, the set point of the secondary controller is communicated backward to the primary controller via the TRO-TRI communication link. The status notification puts the primary PID into an initialization mode. This forces the primary controller output to be the same as the secondary controller set point. (The secondary controller should be configured so that its set point tracks its measurement whenever it is in manual.)... 

Figure 5 Process responses (a) disturbance rejection and (b) set point tracking...

In set point tracking, the set point for the controller is changed and the control objective is to bring the process to the new set point as quickly as possible (see Figure 5(b)). For a person in the shower who wants to reduce the temperature at the end of the shower time, this means turning the hot water tap down to reduce the flow rate of hot water, thereby bringing the temperature down to the new desired level. 

Figure 7 Closed loop responses of first-order process, (a) P only (set point tracking), (b) P only (disturbance rejection), (c) stable PI or PID (disturbance rejection) and (d) unstable PI or PID (disturbance rejection).

How do we choose the values of the controller parameters Kc, ii and td They must be chosen to ensure that the response of the controlled variable remains stable and returns to its steady-state value (disturbance rejection), or moves to a new desired value (set point tracking), quickly. However, the action of the controller tends to introduce oscillations. 

In this work, the influences of two different sets of manipulated inputs have been compared in the case of linear model predictive control of a simulated moving bed. The first one consisting in direct manipulation of flow rates of the SMB showed a very satisfactory behavior for set point tracking and feed disturbance rejection. The second one consists in manipulating the flow rates ratios over each SMB section. At the identification stage, this strategy proved to be more delicate as the step responses displayed important dynamic differences of the responses. However, when the disturbance concerns the feed flow rate, a better behavior is obtained whereas a feed concentration disturbance is more badly rejected. 

In this paper we describe the application of an adaptive network based fuzzy inference system (ANFIS) predictor to the estimation of the product compositions in a binary methanol-water continuous distillation column from available on-line temperature measurements. This soft sensor is then applied to train an ANFIS model so that a GA performs the searching for the optimal dual control law applied to the distillation column. The performance of the developed ANFIS estimator is further tested by observing the performance of the ANFIS based control system for both set point tracking and disturbance rejection cases. 

V.17 Design the steady-state and dynamic feedforward controllers (for disturbance rejection and set point tracking) for the systems with the following transfer functions (transfer function between manipulation and controlled output Gd is the transfer function between disturbance and controlled output). Assume that Gm - Gf = 1. 

Set point tracking. The control mechanism should be capable of making the process output track exactly any changes in the set point (i.e., keep y = ySp). This implies that the coefficient of ySp in eq. (21.11) should be equal to 1 ... 

The following specifications are also given (1) use a PI controller for the feedback loop, and (2) the feedforward system should have both disturbance rejection and set point tracking capabilities... 

Rohani et al. (1990) postulated that it may be desirable to maintain the fines slurry density at some constant value over a batch run. They experimentally realized an improvement of the final CSD (larger mean size and smaller coefficient of variation) by using a conventional PI controller that manipulated the fines destruction rate to maintain a set point for the fines slurry density. Rohani and Bourne (1990) used simulations to demonstrate a selftuning regulator to be more effective in set-point tracking and disturbance rejection than the PI controller. 

A filter is used in the control system to ensure robustness in performance. The exit-air temperature is used for set-point tracking by the IMC. If the system is performed without any oscillations, the overshoots will be tolerable, there will be no offset, and the control scheme will be effective and respond rapidly as described by Panda [19]. 

The choice of the manipulated variables imposes a constraint on all incoming material to a particular node. The PID controllers are tuned to allow for fast set-point tracking and good disturbance rejection dynamics, taking into consideration the transportation delay between nodes. 

The expectance that the dynamic properties of Petlyuk columns may cause control difficulties, compared to the rather well-known behavior of the conventional direct and indirect sequences for the separation of ternary mixtures, has been one of the factors that has contributed to their lack of industrial implementation. In this work, we analyze the closed-loop behavior of Petlyuk columns when a proportional-integral controller with dynamic estimation of unknown disturbances is implemented (Alvarez-Ramirez et al., 1997). The performance of the integrated column under such a controller is compared to the behavior under a traditional proportional-integral controller. The analysis is based on rigorous dynamic simulations, and two cases are considered (i) set point tracking and (ii) output regulation under load disturbances in the feed mixture. 

For the case of set point tracking, the responses of the system under the action of either the PII controller or the traditional PI controller were not significantly different, although the use of the PII controller provided generally a faster adjustment with fewer oscillations. When the response of the column to feed disturbances was analyzed, the PII controller provided a remarkable improvement over the use of the PI controller while in several cases the implementation of the PI controller yielded extremely high... 

The control of a Petlyuk column with a proportional-integral controller with dynamic estimation of uncertainties was analyzed. The dynamic behavior of this action was compared to the Petlyuk column performance under a proportional-integral controller. Set point tracking and responses to feed composition disturbances were analyzed. The results obtained for three case studies show that, after optimizing the controller parameters of each control policy, the closed loop behavior under the Ptf control mode was significantly better than the responses obtained with a PI controller. The superiority of the PII control option was particularly noticeable when the column was subjected to feed disturbances. The properties of the PII controller allow a proper detection of disturbances and a proper corrective action to prevent the controlled output from significant deviations from the desired operation point. In general, the Ptf controller has been found to have an excellent potential for the control of the Petlyuk column. 

In the third step, the attainable performance for the seven remaining structures was computed by quadratic optimization. The optimization goals were set-point tracking and decoupling. The cost function consisted of the sum of the squared regulation errors of all outputs for individual unit steps of the two reference inputs. To meet the input constraints, the manipulated variables were restricted to the ranges shown in Table 8. 

The linear controller is able to deal with the model uncertainties well. For brevity, set-point tracking with the controller is not shown here but it can be stated that the controller is able to deal with significant changes in the set-points over the complete batch. 

Panda investigated the performance of IMC in fluid-bed drying of sand particles, mustard seeds, and wheat grains [19], The structure of the IMC system for the fluid-bed dryer is depicted in the block diagram shown in Figure 49.6. In this study, IMC uses a process-model transfer function (Gm) parallel to the actual plant transfer function (Gp). A filter is used in the control system to ensure robustness in performance. The exit-air temperature is used for set-point tracking by the IMC. If the system is performed without any oscillations, the overshoots will be tolerable, there will be no offset, and the control scheme will be effective and respond rapidly as described by Panda [19]. 

Most of the literature in control of continuous crystallizers is based on a singleinput single output (SISO) control structure. Different controlled variables and manipulations have been suggested based on the relative ease and accuraey of on-line measurements and their efficiency in effectively addressing set-point tracking and disturbance rejections. Both linearized physical models and blackbox models have been suggested for the controller design, as reviewed by Sheikh (1997) as follows. 

Rapid, smooth responses to set-point changes are obtained, that is, good set-point tracking... 

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