Closedloop performance

To quantify this effect, jacket thickness hj is changed from 0.1 down to 0.025 m. The 350 K reactor temperature with 85% conversion is the case studied. Figure 3.21 shows the effect on the Nyquist plot. The improvement in controllability is indicated by the curves dropping more into the third quadrant as hj is decreased. The ultimate gain increases from 8.51 to 17.1 to 24.8. The ultimate period decreases from 2711 to 1846 to 1429 s. These indicate improved closedloop performance. Figure 3.22 shows this to be true. The Tyreus-Luyben settings are used in the three cases. 

Before we design controllers in the frequency domain, it might be interesting to see what the frequency-domain indicators of closedloop performance turn out to be when the Ziegler-Nichols settings are used on this system. Table 11.1 shows the phase... 

Then in Chaps. 7 and 8 we will look at closedloop systems. Instrumentation hardware, controller types and performance, controller tuning, and various types of control systems structures will be discussed. 

PERFORMANCE OF FEEDBACK CONTROLLERS 7.2.1 Specifications for Closedloop Response... 

There are a number of criteria by which the desired performance of a closedloop system can be spedlied in the time domain. For example, we could specify that the closedloop system be critically damped so that there is no overshoot or oscillation. We must then select the type of controller and set its tuning constants so that it will give, when coupled with the process, the desired closedloop response. Naturally the control specification must be physically attainable. We cannot make a Boeing 747 jumbo jet airplane behave like an F-IS fighter. We cannot... 

This system also is a good illustration of the improvement in dynamic performance that cascade control can provide in some systems. As we will show quantitatively in Chap. 11, the closedloop time constant of the reactor temperature will be smaller when the cascade system is used than when reactor temperature sets the cooling water makeup valve directly. Therefore performance has been improved by using cascade control. 

In this chapter we will demonstrate the signiScant computational and nota-tional advantages of LaplaTce transforms. The techniques involve finding the transfer function of the openloop process, specifying the desired performance of the closedloop system (process plus controller) and finding the feedback controller transfer function that is.required to do the job. 

Normally we design the feedback controller flj,) to give some desire closed-loop performance. For example, we might specify a desired closedloop damping coefficient. 

In order to design feedback controllers, we must have some way to evaluate their effect on the performance of the closedloop system, both dynamically and at steadystate. 

The dynamic performance of a system can be deduced by merely observing the location of the roots of the system characteristic equation in the s plane. The time-domain specifications of time constants and damping coefficients for a closedloop system can be used directly in the Laplace domain. 

We would like to compare the closedloop dynamic performance of two types of reboilers. 

Up to this point we have usually chosen a type of controller (P, PI, or PID) and determined the tuning constants that gave some desired performance (closedloop damping coefneient). We have used a model of the process to calculate the controller settings, but the structure of the model has not been explicitly involved in the controller design. 

The F factor is varied until L ls equal to 2N, where N is the order of the system. For N = 1, the SISO case, we get the familiar -f2 dB maximum closedloop log modulus criterion. For a 2 x 2 system, a +4 dB value of is used for a 3 x 3, -1-6 dB and so forth. This empirically determined criterion has been tested on a large number of cases and gives reasonable performance, which is a little on the conservative side. 

These parameters are varied to achieve some desired performance criteria. In the z-plane root locus plots, the specifications of closedloop time constant and damping coefficient are usually used. The roots of the closedloop characteristic equation 1 -I- are modified by changing. ... 

Up to this point we have dealt with processes which give worse control performance when sampled-data control is used than when continuous control is used. We have demonstrated this effect quantitatively by showing that ultimate gains and gains that give a desired closedloop damping coefficient decrease as T, is increased. 

Unfortunately the sampled-data controller is really not better than the continuous. The controller gain that gives 4- 2 dB maximum closedloop log modulus for the continuous controller is 1.95. The corresponding gain for a sampled-data controller with a sampling period of 1.1 is only 1.73. In addition, the sampled-data controller will not detect load disturbances as quickly as the continuous. So the performance of the sampled-data controller is not as good as the continuous. 

These three nonlinear ordinary differential equations will be used to simulate the dynamic performance of the CSTR. The openloop behavior applies when no controllers are used. In this case the flowrate of the cooling water is held constant. With closedloop behavior, a temperature controller is installed that manipulates cooling water flow to maintain reactor temperature. 

Cascade control was discussed qualitatively in Section 4.2. It employs two control loops the secondary (or slave ) loop receives its setpoint from the primary (or master ) loop. Cascade control is used to improve load rejection and performance by decreasing closedloop time constants. 

This is a design whose time has really come with the advent of high-performance closedloop servo drives and the use of computers as system controllers. Feed rolls should be considered if your parts have complex hole patterns with many dimensional variations. Traditionally, multiple dies and very large presses would be required. The more common arrangement for this type of system is shown in Fig. 19. The punch tools inside the die are selectable by moving blocks over the... 

Dynamic fundamentals The importance of designing processes and establishing loop pairing to minimize undesirable dynamics in a feedback loop is obvious to an engineer who xmderstands the effects of deadtime, multiple lags and inverse response on the stability and performance of a closedloop system. 

In chemical engineering the typical steady-state economic performance parameters are capital investment and energy cost. The smaller these numbers, the more efficient the process. The typical dynamic performance parameter is the closedloop time constant. The smaller this number, the more quickly disturbances can be attenuated and the faster the process can be transitioned to some new operating condition. A short list of some examples of the conflict between steady-state and dynamic objectives is given below. 

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