Signal Processing and Linear Systems-B.P.Lathi copy

T he gains of 2 and 5 required in the feedforward

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Unformatted text preview: his case is exactly equal to the input signal itself because G H = 1. Hence, once a signal is applied, no m atter how small and how short in duration, it comes back t o reinforce the input undiminished, which further passes t o t he o utput, a nd is fed back again and again and again. In essence, t he signal perpetuates itself forever. This perpetuation, even when the input ceases t o exist, is precisely the symptom of instability. 6 .7-1 Analysis o f a Simple Control System O __ _ G T - 1 + GH = 20,000 1 + 200 = 99.5 Observe t hat 100% variation in the forward gain G causes only 0.5% variation in the feedback amplifier gain T . Y ( /) F ig. 6 .35 Effects o f p ositive a nd n egative feedback. 'd h at h appens when we a dd (instead of subtract) t he si~nal. fed Now, consl e r w .. h i n on the feedback connectiOn IS + back to the inpu~. S.uch addltiOchn me~ns t~ e ~ g of H in Fig. 6.35). Consequently instead of - (whIch IS same as angillg e Sign G T= I f we let G 1-Gii = 1 0,000 as before and H = 0.9 X 1 0- Ts _ K G(s) ( )-l+KG(s) From this equation, we shall investigate the behavior of the automatic position control system in Fig. 6.36a for a s tep and a ramp input. 4 , t hen 10,000 = 100,000 1 _ 0.9(10 4)(10 4) . I e ment of some transistors, the gain of the g Suppose t hat .bfiecauhse of a ill: o~O~ep~e new gain of the feedback amplifier is 1, forward ampli e r c anges t 0 . T= 11,000 = 1,100,000 T = 1 _ 0.9(11,000)(10 4) .' ? bserve ~hat ill t~~ illcrease ill t he g a Figure 6.36a represents an automatic position control system, which can be used to control t he a ngular position of a heavy object (e.g., a tracking antenna, an anti-aircraft gun mount, or the position of a ship). The input ()i is the desired angular position o f t he object, which can be set a t a ny given value. T he a ctual angular position ()o o f the object (the o utput) is measured by a potentiometer whose wiper is m ounted on t he o utput shaft. The difference between the o utput ()o a nd the input ()i is amplified; t he amplified o utput, which is p roportional t o ()o - ()i, is applied to the motor input. I f ()o - ()i = 0 ( the o utput being equal t o t he desired angle), there is n o input to the motor, and t he m otor stops. B ut if ()o f. ( )i, t here will be a nonzero input t o t he motor, which will t urn t he shaft until ()o = ( )i. I t is evident t hat by setting the input potentiometer a t a desired position in this system, we c an control the angular position of a heavy remote object. T he block diagram of this system is shown in Fig. 6.36b. T he amplifier gain is K , where K is a djustable. Let the motor (with load) transfer function t hat r elates the o utput angle ()o to the motor input voltage be G(s) [see Eq. (1.65)J. This feedback arrangement is identical to t hat in Fig. 6.18d with H (s) = 1. Hence, T (s), t he (closed-loop) system transfer function relating the o utput ()o t o t he input ( )i, is ere 10% increase in the forward gain G caused 1000% 100,000 t o 1,100,000). Clearly, the amplifier is very . t' T his behavior is exactly opposite of what was ~(~~:m ~~:~:~:~ ::fi::~~~~e~ t;:I~~~:rfed back was subtracted from the input. S tep Inpu...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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