Module 3. Process Control. Version 2 EE IIT, Kharagpur 1

Transcription

1 Module 3 Process Control Version 2 EE IIT, Kharagpur 1

2 Lesson 15 Special Control Structures: Feedorward and Ratio Control Version 2 EE IIT, Kharagpur 2

3 Instructional Objectives At the end o this lesson, the student should be able to Justiy the use o eedorward controller in addition to conventional eedback controller. Draw the block diagram o a eedorward-eedback controller. Find the transer unction o the eedorward controller or complete disturbance rejection. Write down three typical applications o ratio control Give two possible arrangements or achieving ratio control Introduction In the last ew lessons we have discussed about the dierent aspects o PID controllers, their tuning, implementation etc. In all the cases the control action considered was eedback type; i.e. the output was ed back and compared with the set point and the error was ed to the controller. The output rom the controller was used to control the manipulating variable. However there are several cases, where apart rom the eedback action ew other control structures are incorporated in order to satisy certain requirements. In this lesson we would take up two such special control structures: eedorward and ratio control. Feedorward Control When the disturbance is measurable, eedorward control is an eective means or cancelling the eects o disturbance on the system output. This is advantageous, since in a simple eedback system, the corrective action starts ater the eect o disturbance is relected at the output. On the other hand, in eedorward control the change in disturbance signal is measured and the corrective action takes place immediately. As a result, the speed and perormance o the overall system improves, i eedorward control, together with eedback action is employed. In order to illustrate the eect o eedorward control, let us consider the heat exchange process shown in Fig.1. The cold water comes rom a tank and lows to the heat exchanger. The low rate o cold water can be considered as a disturbance. The change in input low line may occur due to the change in water level in the tank. Suppose, the eedorward line is not connected, and the controller acts as a eedback control only. I the water inlet low rate increases, the temperature o the outlet hot water low will decrease. This will be sensed by the temperature sensor that will compare with the set point temperature and the temperature controller will send signal to open the control valve to allow more steam at the steam inlet. The whole operation is a time consuming and as a result the response o the controller due to the disturbance (inlet water low rate) is normally slow. But i we measure the change in inlet low rate by a lowmeter and eed this inormation to the controller, the controller can immediately take the correcting action anticipating the change in outlet temperature. This will improve the speed o response. Thus eedorward action, in addition to the eedback control improves the perormance o the system, but provided, the disturbance is measurable. Version 2 EE IIT, Kharagpur 3

4 Let us now draw the block diagram o the overall control operation o the system shown in Fig. 1. The block diagram representation is shown in Fig. 2. In general, the structure o the eedorward-eedback action in terms o the block diagram o transer unctions can be represented as shown in Fig. 3. Where, Gs () = Transer unction o the process (manipulating variable to output) G () n s = Disturbance transer unction (disturbance to output) Gc( s) = Transer unction o eedback controller Version 2 EE IIT, Kharagpur 4

5 G () s = Transer unction o the eedorward controller So there are two controllers, one is the conventional eedback controller Gc( s), while the other is the eedorward controller that is intended to nulliy the eect o disturbance at the output. From Fig. 3, the overall output is: C(s) = G c( s)g(s) E(s) +G n( s) N(s) = G ( s)g(s) R(s)-C(s) +G N(s) G (s) N(s) [ ] + [ ] [ s ] c n c s + c n =G ( )G(s) R(s)-C(s) G ( )G(s)G (s) +G (s) N(s) I we want to select the eedorard transer unction, such that, the eect o disturbance at the output is zero, then we require the co-eicient o N(s) in above equation to be set to zero. Thus, G()G(s)G(s)+G(s)=0 c s n G n (s) or, G(s)=- (1) G (s)g(s) c It is to be noted that complete disturbance rejection can be obtained i the transer unctions G p (s) and G n (s) are known accurately, which is not possible in actual situation. As a result, the perormance o the eedorward controller will deteriorate and complete disturbance rejection can not be achieved, through the eect can be reduced considerably. However the eedback controller would reduce the residual error due to imperect eedorward control and at the output, the eect o imperect cancellation may not be elt. Example -1 Consider the composition control system o a certain reagent. The block diagram o the eedorward-eedback control system is shown in Fig.4. Here we are using a P-I controller or eedback action. C i is the disturbance signal. Compared to Fig.3, the eedorward controller Version 2 EE IIT, Kharagpur 5

6 output in the present case is added ater the eedback controller. Suppose, the plant transer unction and the disturbance transer unction are given by: 1 G(s) p = 3 (s+1) 1 G n (s) = 3 (5s+1)(s+1) With a little calculation using eqn.(1), we obtain the transer unction o the eedorward controller as: 1 G(s) = 5s+1 But in many cases, practical implementation o the eedorward controller as obtained rom eqn.(1) is diicult. It can be easily seen in the above example i the disturbance transer unction is : 1 G n (s) = 2 (s+1) In this case, the eedorward controller transer unction becomes: G(s) = (s+1) But since the above transer unction is not a proper one, practical realization o this transer unction is diicult. In these cases, the transer unction o the eedorward controller is chosen in the orm o a lag-lead compensator as: K(1+Ts) 1 G(s) =, with T 2<<T 1 and K is a constant. (1+T s) 2 In the present case the transer unction G(s) = (s+1) can be realized by approximating as: s+1 G(s) =. 0.1s+1 In normal case, the transer unction o the process is not known exactly. So the question is how to tune the parameters o the eedorward controller or optimum perormance. This can be carried out by perorming some experimentation or tuning the controller. The details o the tuning procedure or eedorward controllers can be ound in [2]. Version 2 EE IIT, Kharagpur 6

7 Ratio Control Ratio control is a special type o eedorward control where the disturbance is measured and the ratio o the process output and the disturbance is held constant. It is mostly used to control the ratio o low rates o two streams. Flow rates o both the stream are measured, but only one o them is controlled. There can be many examples o application o ratio control. Few examples are: 1. uel-air ratio control in burners, 2. control o ratio o two reactants entering a reactor at a desired ratio, 3. maintaining the ratio o two blended streams constant in order to maintain the composition o the blend at the desired value. There can be two schemes or achieving ratio control. The irst scheme is shown in Fig. 5. In this coniguration the ratio o low rates o two streams is measured and compared with the desired ratio. The error is ed to the controller and the controller output is used to control the low rate o stream B. The second possible scheme or ratio control is shown in Fig. 6. Suppose the low rate o luid B has to be maintained at a constant raction o low rate o luid A, irrespective o variation o low rate o A (q A ). In this scheme the low rate o luid A is multiplied with the desired ratio (set externally) that gives the desired low rate o luid B. This is compared with the actual low rate o luid B and ed to the controller that operates the control valve. Version 2 EE IIT, Kharagpur 7

8 Suppose that the above scheme (Fig. 6) is used or controlling the uel-air ratio in a burner where airlow rate (luid B) is controlled. But the desired ratio is also dependent on the temperature o the air. So an auxiliary measurement is needed to measure the temperature o air and set the desired ratio. Such a scheme is shown in Fig. 7. Version 2 EE IIT, Kharagpur 8

9 The controllers in ratio control are usually P-I type. This is in order to achieve zero steady state error or maintaining the desired ratio. Derivative action is avoided because the low is always noisy. Example -2 We have mentioned earlier that ratio control is a special type o eedorward control. We shall elaborate this point in the ollowing example [4]. Eects o control actions in eedback only mode, eedorward only mode and eedorward-eedback mode will also be elaborated in the context o control o a blending process. Consider a blending system where two streams are blended; one is uncontrolled wild stream that acts as disturbance and another is controlled and acts as the manipulated variable. The ratio o these two streams aect the quality o the output o the process. Version 2 EE IIT, Kharagpur 9

10 First consider a simple eedback system shown in Fig. 8(a). The composition o the output stream is unmeasured and ed to the composition controller that controls the low rate o the manipulated stream. But the perormance o this system may not be satisactory, since any variation o the wild stream will cause the change in composition o the output, that will be elt ater certain time. As a result the perormance o the eedback controller is sluggish. Version 2 EE IIT, Kharagpur 10

11 On the other hand the perormance o the blending process can be made considerably aster i he incorporate the ratio control scheme as shown in Fig. 8(b). In this case, the disturbance (low rate o wild stream) is measured and corrective action is taken immediately by controlling manipulated stream so as to maintain a constant ratio between them. It is evident that this the control action is eedorward only, since the composition o the output stream is not unmeasured. But the above scheme also suers rom certain limitations, since the composition variation due to other disturbances is not taken into account. So though aster, i may not yield the desired perormance. The perormance may be urther improved by choosing a eedorward-eedback control scheme (Fig. 8(c)) where the composition o the output stream is measured and the composition controller sets the desired ratio to be maintained. Reerences 1. G. Stephanopoulus: Chemical process Control, Prentice Hall o India, New Delhi, D.R. Coughanowr: Process systems analysis and control (2/e), McgrawHill, NY, K. Ogata: Modern Control Engineering (2/e), Prentice Hall o India, New Delhi, W.L. Luyben and M.L. Luyben: Essentials o Process Control, McgrawHill, NY, Review Questions 1. When would you recommend the use o eedorward controller? What is the advantage o using this control? 2. Draw the general block diagram o a eedorward-eedback control scheme and develop the transer unction o the eedback controller. 3. What modiication o the transer unction o the eedorward controller is suggested when the obtained transer unction o the controller is not proper? 4. Explain with an example the principle o ratio control. Elaborate with a block diagram any one scheme or achieving ratio control. 5. Why the controller used or ratio control is normally P-I type? Version 2 EE IIT, Kharagpur 11