Cohen-Coon controller settings

Cohen and Coon observed that the response of most uncontrolled (controller disconnected) processes to a step change in the manipulated variable is a sigmoidally shaped curve. This can be modelled approximately by a first-order system with time lag Tl, as given by the intersection of the tangent through the inflection point with the time axis (Fig. 2.34). The theoretical values of the controller settings obtained by the analysis of this system are summarised in Table 2.2. The model parameters for a step change A to be used with this table are calculated as follows 

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Cohen-Coon controller settings 103, 508 Coils or jackets 132 Column hydrodynamics 195... 

Using the first order with dead time function, we can go ahead and determine the controller settings with empirical tuning relations. The most common ones are the Ziegler-Nichols relations. In process unit operation applications, we can also use the Cohen and Coon or the Ciancone and Marlin relations. These relations are listed in the Table of Tuning Relations (Table 6.1). 

In this illustration, we do not have to detune the SISO controller settings. The interaction does not appear to be severely detrimental mainly because we have used the conservative ITAE settings. It would not be the case if we had tried Cohen-Coon relations. The decouplers also do not appear to be particularly effective. They reduce the oscillation, but also slow down the system response. The main reason is that the lead-lag compensators do not factor in the dead times in all the transfer functions. 

Proportional gain, integral and derivative time constants to PI and PID controllers. Cohen-Coon was designed to handle disturbances by preventing a large initial deviation from the set point. The one-quarter decay ratio response is generally too underdamped for set point changes. 

Determine the open-loop response of the output of the measuring element in Problem 7.17 to a unit step change in input to the process. Hence determine the controller settings for the control loop by the Cohen-Coon and ITAE methods for P, PI and PID control actions. Compare the settings obtained with those in Problem 7.17. 

Referring to Exercise 1, use Cohen-Coon settings from Table 2.2 to obtain the best controller settings for P and PI control from the process reaction curve parameters. Try these out in a simulation. Observe the suitability of the settings from the error e and the integral of its square, EINT2. 

Discuss the philosophy of the methodology that leads to the Cohen-Coon settings for feedback controllers. 

Cohen-Coon settings (see Section 16.5) From the process reaction curve we can estimate the process static gain K, the dominant time constant r, and the process dead time td Then, from eqs. (16.9) through (16.11c), we can compute the parameters Kc, r/, and rD of a P, PI, or PID control algorithm. The effect of the sampling period T has been accounted for by the nature of the experiment itself, because the reaction curve has been determined using sampled-values of the process output. 

The Ziegler-Nichols settings result from closed-loop considerations, whereas the Cohen-Coon settings are determined from the open-loop response of the control system. Would you choose one over the other because it uses open- or closed-loop data Explain. 

Compute the settings of a PID controller using the Cohen-Coon tuning methodology. 

IV.44 Consider the feedback loop shown in Figure PIV.3a. Select the settings of the PI controller using the Cohen-Coon tuning technique. In a graph paper display the actual process reaction curve and its first-order plus dead time approximation. 

VII.36 (a) Design a digital PI controller in velocity form, using the Cohen-Coon settings. The experimental process reaction curve was developed with a sampling period of 0.2 min and is given in Table PIV. 1. 

Choosing the Controller Setting According to COHEN and COON... 

You are required to design two cylindrical tanks in series to supply a chemical plant with a constant water feed of 35 m /h. The feed to the first tank keeps fluctuating, whereas the feed to the plant needs to be constant at 35 m /hr. Design a suitable control loop (PI control action) for this system. Draw appropriate block diagrams for both the open- (uncontrolled) and closed- (controlled) loop cases. Find the optimal control settings (gains) using the decay ratio criterion, and the Cohen and Coon criterion and compare the results of both methods. 

Table 32.2. PID Controller settings according Cohen-Coon.

The Cohen-Coon recommended controller settings are as follows ... 

All tuning relations provide different results. Generally, the Cohen and Coon relation has the largest proportional gain and the dynamic response tends to be the most underdamped. The Ciancone-Marlin relation provides the most conservative setting, and it uses a very small derivative time constant and a relatively large integral time constant. In a way, their correlation reflects a common industrial preference for PI controllers. 

Another published method frequently quoted is that by Cohen and Coon (Reference 6). It too uses the quarter decay criterion and is presented as sets of formulae based on process dynamics. For P only control... 

In 1953, Cohen and Coon [2] developed a set of controller tuning recommendations that correct for one deficiency in the Ziegler-Nichols open-loop rules. This deficiency is the sluggish closed-loop response given by the Ziegler-Nichols rules on the relatively rare occasion when process dead time is large relative to the dominant open-loop time constant. 

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