Closed-Loop Feedforward Systems

Closed loop systems inelude either a feedbaek or feedforward, eontrol loop or both to eontrol the plant. In a feedbaek eontrol loop, the eontrolled variable is eompared to a set point. The differenee between the eontrolled variable to the set point is the deviation for the eontroller to aet on to minimize the deviation. A feedforward eontrol system uses the measured load or set point to position the manipulated variable in sueh a manner to minimize any resulting deviation. 

Our next task is to find the closed-loop transfer functions of this feedforward-feedback system. Among other methods, we should see that we can "move" the G vGp term as shown in Fig. 

Thus we have described a system and process having a multiplicity of iterative feedbacks and feedforwards from each component and subprocess, to every other component and subprocess, all increasing the energy collected in the system and furnished to the load. In open-loop operation, this results in COP >1.0 permissibly, since the excess energy is freely received from an external source. In closed-loop operation, the COP concept does not apply except with respect to operational efficiency. In that case, the operational... 

A closed-loop system uses the measurement of one or more process variables to move the manipulated variable to achieve control. Closed-loop systems may include feedforward, feedback, or both. 

Figure 24.3. Feedback and feedforward control systems. In feedback control, a measuring instrument obtains information at the output of a process, the signal obtained is compared to a set point, and the difference (or result) is applied to a final actuator. The result is ultimately detected by the measuring instrument and closed-loop control results. In feedforward control a measuring instrument obtains information at the input of a process, the signal obtained is again compared to a set point, but now the result is applied to an actuator that controls another input to the process. The result is not detected by the measuring instrument and open-loop control results. Courtesy of the Foxboro Company.

A healthy rose plant will bloom with profuse, beautiful flowers. The plant requires water, and therefore must be watered. If water is added without regard to the condition of the plant, this is an open-loop system. If water is added only when the plant needs it, or if the amount varies to meet plant moisture requirements, then the system is closed-loop with feedback. If extra water is added because you will be unable to care for the plant for a few days, then this is a feedforward control system. 

Like any closed-loop system, the behavior of the respiratory control system is defined by the continual interaction of the controller and the peripheral processes being controlled. The latter include the respiratory mechanical system and the pulmonary gas exchange process. These peripheral processes have been extensively studied, and their quantitative relationships have been described in detail in previous reviews. Less well understood is the behavior of the respiratory controller and the way in which it processes afferent inputs. A confounding factor is that the controller may manifest itself in many different ways, depending on the modeling and experimental approaches being taken. Traditionally, the respiratory control system has been modeled as a closed-loop feedback/feedforward regulator whereby homeostasis of arterial blood gas and pH is maintained. Alternatively, the respiratory controller may be viewed as a... 

A different type of closed-loop control is feedforward control, in which optimal controls are explicitly obtained in advance from the inputs in conjunction with the mathematical model of a system. As shown in the above figure, feedforward controls are applied to the system without having to wait for the system state the inputs and controls would later generate. 

From the stability of the inverse (or zero) dynamics motion (Eq. 15) and of the linear filter (Eq. 16b) (tuned sufficiently fast), the stability of the closed-loop system motion follows. The regulated-measured outputs (z, ) have quasi(q)LNPA tracking dynamics, and the unmeasured regulated outputs (Zf) have the Eb-stability property (7) of the ZD motion (Eq. 15). As the controller gain is tuned faster, the controller approaches the behavior of its feedforward counterpart (Eq. 14), and this feature in turn constitutes the behavior recovery target of the measurement -driven controller that will be developed next. 

Although not usually pointed out in the literature, it is also true, as Gould has indicated, that the engineer should be careful not to design a feedback system whose closed-loop natural frequency is within the frequency range of disturbances. Feedforward compensation often may be used instead of feedback to get improved control without problems with either stability or resonance peaks. 

Rippin and Lamb point out that if we provide a perfect feedforward control system to adjust Lr so that feed changes in flow and composition do not change jVr, then the transmission Xr s) is broken and there is no feedback of Xr(s) down the column. It is possible to accomplish the same thing by making l/xp sufficiently smaller than the resonant frequency of the closed-loop composition-control system. This has been shown experimentally by Aikmam to be true of a plant column. The mathematical explanation is simple. 

In Chapter 11 it was shown that the roots of the characteristic equation completely determine the stabihty of the closed-loop system. Because Gf does not appear in the characteristic equation, the feedforward controller has no effect on the stability of the feedback control system. This is a desirable situation that allows the feedback and feedforward controllers to be tuned individually. 

Consider the blending system of Section 15.3, but now assume that a pneumatic control valve and an I/P transducer are used. A feedforward-feedback control system is to be designed to reduce the effect of disturbances in feed composition xi on the controlled variable, product composition X. Inlet flow rate 1V2 can be manipulated. Using the information given below, design the following control systems and compare the closed-loop responses for a +0.2 step change in xi. 

The closed-loop responses to a step change in x fron 0.2 to 0.4 are shown in Fig. 15.13. The set point is the nominal value, Xsp = 0.34. The static feedforward controller for cases (a) and (b) are equivalent and thus produce identical responses. The comparison in part (a) of Fig. 15.1 shows that the dynamic feedforward controller is superior to the static feedforward controller, because it provides a better approximation to the ideal feedforward controller of Eq. 15-33. The PI controller in part (b) of Fig. 15.13 produces a larger maximum deviation than the dynamic feedforward controller. The combined feedforward-feedback control system of part (d) results in better performance than the PI controller, because it has a much smaller maximum deviation and lAE value. The peak in the response at approximately t = 13 min in Fig. 15.13b is a consequence of the x measurement time delay. 

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