Open-loop response

The power applied by die expander to die shaft must be redueed in diis situation. Open-loop eontrol ean be applied, but an intelligent applieation of die open-loop response should be made. How mueh to reduee diis power is deseribed in the following paragraphs. The eharaeteristies deseribed in the seetion Expander eharaeteristies are needed to determine expander power output under any eonditions. 

B.2 Defining the Open Loop Response of the Switching Power Supply—The Control-to-Output Characteristics... 

Study the simple, open-loop (KC = 0) and closed-loop responses (KC = -1 to 5, TSET = TDIM, and 300 to 350 K) and the resulting yields of B. Confirm the oscillatory behaviour and find appropriate values of KC and TSET to give maximum stable and maximum oscillatory yield. For the open-loop response, show that the stability of operation of the CSTR is dependent on the operating variables by carrying out a series of simulations with varying Tq in the range 300 to 350 K. 

This work covers only open loop response. Use of this algorithm alone on a real reactor would presuppose that the model is very precise — that a desired MW and S can be obtained merely by... 

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. 

Set the initial concentration profiles in the two phases equal to the steady state open loop response (Kc= 0), and study the response of the system to another set point change or flow rate change. 

Forcing function is a term given to any disturbance which is externally applied to a system. A number of simple functions are of considerable use in both the theoretical and experimental analysis of control systems and their components. Note that the response to a forcing function of a system or component without feedback is called the open-loop response. This should not be confused with the term open-loop control which is frequently used to describe feed-forward control. The response of a system incorporating feedback is referred to as the closed-loop response. Only three of the more useful forcing functions will be described here. 

Consider the control loop shown in Fig. 7.44. Suppose the loop to be broken after the measuring element, and that a sinusoidal forcing function M sin cot is applied to the set point R. Suppose also that the open-loop gain (or amplitude ratio) of the system is unity and that the phase shift xj/ is -180°. Then the output JB from the measuring element (i.e. the system open-loop response) will have the form ... 

Consider the open-loop response of B to a change in R. Clearly it is desirable that the measured value should consist of current information and not information which has been delayed by the dead time represented by G3(j). Suppose that the measured value without dead time is Bu i.e. that ... 

If B is the open-loop response of the measured value including the dead time, then we can write (Fig. 7.60) ... 

In the following text, important aspects in the study of process dynamics are outlined. An example of a dynamic process is given first. Stability of a process is defined next, followed by a discussion of typical uncontrolled, or open loop, responses. 

Process Reaction Curve Method (Cohen-Coon Tuning). For some processes, it may be difficult or hazardous to operate with continuous cycling, even for short periods. The process reaction curve method obtains settings based on the open loop response and thereby avoids the potential problem of closed loop instability. The procedure is as follows ... 

Figure 12.5 shows an example of a one-dimensional bifurcation diagram for the single-nephron model obtained by varying the slope a of the open-loop response... 

Correlations such as those presented in Table 3.2 may then be used to determine the values of tuning parameters based upon the open-loop response (Edgar, 1999). 

TABLE 3.2. Tuning Parameter Values from Open-Loop Response... 

It should be noted that if the open-loop response is evaluated by numerical integration, there is no requirement for linearity of the process model. Convenient analytical solutions can be found for some linear systems, such as series stirred tanks with instantaneous reaction and constant flow. 

In general, there will be uncertain or variable properties to consider and it will be required that the constraints be satisfied for all combinations of the corresponding uncertain parameters. This uncertainty is assumed to be parameterized by a parameter vector v, the values of which lie within a polyhedron V. V may include both parameters defining the possible disturbances and model parameters affecting the initial open-loop response, such as biases on measurements used for control. 

The number of uncertain parameters required to model uncertainty is reduced as some parameters, such as those associated with measurement dynamics, do not affect the open-loop response. 

In Fig. 1(B) one can observe that the parametric controller of order p= 0 improves the response when compared with the open loop response, as expected for this class of full-scale parametric controllers. For order p = 6 (Fig. 1(C)), there is an initial strong response from the controller which makes its performance of inferior quality by comparison to cases A and B. Nevertheless, it stabilizes the states. However, controller p=3 (Fig. 1(D)) shows a poor performance as a consequent of significant model reduction. 

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... 

FIGURE 15.61 Open-loop response for a heat exchanger for different feed rates. 

The system in Figure 13.1a is known as open loop, in contrast to the feedback-controlled system of Figure 13.1b, which is called closed loop. Also, when the value of d or m changes, the response of the first is called open-loop response while that of the second is the closed-loop response. The origin of the term closed-loop is evident from Figure 13.1b. 

The time constant has been reduced (i.e., x < xp), which means that the closed-loop response has become faster, than the open-loop response, to changes in set point or load. 

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. 

Unlike the process reaction curve method which uses data from the open-loop response of a system, the Ziegler-Nichols tuning technique is a closed-loop procedure. It goes through the following steps ... 

The gain margin and phase margin of an open-loop response can also be computed from a Nyquist plot. This should be expected since Bode and Nyquist plots of a system contain exactly the same information. 

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