Process control open loop response

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. 

There are a couple of simple empirical approaches for estimating the optimum controller settings for a particular process. Both approaches require data on the response of the existing process to simple stimuli one the open-loop response to a step the other the behavior of the closed-loop at the condition of ultimate gain. 

For slow-response loops (e.g., certain temperatnre and composition control loops), field tuning can be a time-consuming procednre that leads to less than satisfactory resnlts. Step test results can be used to generate FOPDT models, and tnning parameters can be calcnlated from a variety of techniques. This approach suffers from the fact that it takes approximately the open-loop response time of the process to implement a step test, and during that time, measured and unmeasured disturbances can affect the process, thus corrupting the results from the step test. In addition, it is unlikely that the selected turfing approach will result in the proper balance between reliability and... 

To use the Bode criterion, we need the Bode plots for the open-loop transfer function of the controlled system. These can be constructed in two ways (a) numerically, if the transfer functions of the process, measuring device, controller, and final control element are known and (b) experimentally, if all or some of the transfer functions are unknown. In the second case the system is disturbed with a sinusoidal input at various frequencies, and the amplitude and phase lag of the open-loop response are recorded. From these data we can construct the Bode plots. 

Since most of the chemical processes exhibit an open-loop response which can be approximated by a first-order system with dead time, it is clear that the possibility for closed-loop instability will, almost always, be present. Therefore, the tuning of the feedback controller becomes a crucial task. 

The reaction-curve method is based on the open-loop response of the process to a step input. This response curve can be used to derive the dynamic characteristics of the process. If the process can be described by a first-order lag and dead time, the controller setting can be calculated. 

Oscillation in the step response is rare for chemical processes under open-loop or manual conditions. When feedback control is implemented, with processes described by cases 2-6, the occurrence of oscillation is quite common. In fact, a weU-tuned feedback controller exhibits some degree of oscillation, as discussed later. The time constants for this case are not real values but are imaginary numbers. 

A qualitative appraisal of the requirement for dynamic compensation may be obtained from a comparison of open-loop response curves. Because an increase in the manipulated variable acts in opposition to the load, their individual stq>reqx)nse curves will diverge. One or the other response will have to be inverted so that the two curves may be supaimposed, as is done in Fig. 8.10. The response of such a process under uncompensated feedforward control appears as the difference between these two curves. 

Step 1. Adjust Kf. The effort required to tune a controller is greatly reduced if good initial estimates of the controller parameters are available. An initial estimate of Kf can be obtained from a steady-state model of the process or from steady-state data. For example, suppose that the open-loop responses to step changes in d and u are available, as shown in Fig. 15.15. After Kp and K have been determined, the feedforward controller gain can be calculated from the steady-state version of Eq. 15-21 ... 

The responses for yi, y2, and so on are then observed. All loops are kept open during this test that is, no feedback controllers are operational. Then step changes can be made in the other inputs, one at a time, and open-loop response data can be obtained for all the controlled variables. The steady-state gain depends only on the final value of each y, from which the change in y, Ay, can be calculated. Thus, the individual process gains are given by the formula (see Chapter 7) ... 

Open-Loop versus Closed-Loop Dynamics It is common in industry to manipulate coolant in a jacketed reacdor in order to control conditions in the reacdor itself. A simplified schematic diagram of such a reactor control system is shown in Fig. 8-2. Assume that the reacdor temperature is adjusted by a controller that increases the coolant flow in proportion to the difference between the desired reactor temperature and the temperature that is measured. The proportionality constant is K. If a small change in the temperature of the inlet stream occurs, then depending on the value or K, one might observe the reactor temperature responses shown in Fig. 8-3. The top plot shows the case for no control (K = 0), which is called the open loop, or the normal dynamic response of the process by itself. As increases, several effects can be noted. First, the reactor temperature responds faster and faster. Second, for the initial increases in K, the maximum deviation in the reactor temperature becomes smaller. Both of these effects are desirable so that disturbances from normal operation have... 

To make use of empirical tuning relations, one approach is to obtain the so-called process reaction curve. We disable the controller and introduce a step change to the actuator. We then measure the open-loop step response. This practice can simply be called an open-loop step test. Although we disconnect the controller in the schematic diagram (Fig. 6.1), we usually only need to turn the controller to the manual mode in reality. As shown in the block diagram, what we measure is a lumped response, representing the dynamics of the blocks Ga,... 

One reason why this approximation works is that process unit operations are generally open-loop stable, and many are multi-capacity in nature. Reminder Underdamped response of the system is due to the controller, which is taken out in the open-loop step test. 

Another advantage of frequency response analysis is that one can identify the process transfer function with experimental data. With either a frequency response experiment or a pulse experiment with proper Fourier transform, one can construct the Bode plot using the open-loop transfer functions and use the plot as the basis for controller design.1... 

INFICON s Auto Control Tune is based on measurements of the system response w/ith an open loop. The characteristic of the system response is calculated on the basis of a step change in the control signal. It is determined experimentally through two kinds of curve accordance at two points. This can be done either quickly w/ith a random rate or more precisely with a rate close to the desired setpoint. Since the process response depends on the position of the system (in our case the coating growth rate), it is best measured near the desired virork point. The process information measured in this vray (process amplification Kp, time constant T., and dead time L) are used to generate the most appropriate PID control parameters. 

General Second-Order Element Figure 8-3 illustrates the fact that closed-loop systems can exhibit oscillatory behavior. A general second-order transfer function that can exhibit oscillatory behavior is important for the study of automatic control systems. Such a transfer function is given in Fig. 8-15. For a unit step input, the transient responses shown in Fig. 8-16 result. As can be seen, when t, < 1, the response oscillates and when t, < 1, the response is S-shaped. Few open-loop chemical processes exhibit an oscillating response most exhibit an S-shaped step response. 

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