Automatic control systems kuo solution manual 7th edition

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Also, the current is changing with the rate of changes in displacement. Substituting equation 3 , 4 , 5 and 6 into equation 7 and 8 gives the model of the system.

The state model of the system is given by substituting equations 2 , 3 , and 6 into these equations give. The state equations can be rewritten by substituting P2, Pv, Ps and Q2-v from other equations. Thus, N 9. See Chapter 6. Thus e ss f. Since the system is linear, then the effect of X s is the summation of effect of each individual input. Thus Z n Thus, Z n Thus Kt 0.

Z n The coefficients are ordered in descending powers. Other parts are the same. For description refer to Chapter 9. Therefore the natural frequency range in the region shown is around 2. Overshoot increases with K. No need to adjust parameters. For the sake simplicity, this problem we assume the control force f t is applied in parallel to the spring K and damper B.

We will not concern the details of what actuator or sensors are used. Lets look at Figure and equations and This is now an underdamped system. The process is the same for parts b, c and d. Use Example as a guide. Use Acsys to do that as demonstrated in this chapter problems. Also Chapter 2 has many examples. You may look at the root locus of the forward path transfer function to get a better perspective. For a better design, and to meet rise time criterion, use Example 5- Open loop speed response using SIMLab: a.

Considering an amplifier gain of 2 and K b 0. Study of the effect of viscous friction: The above figure is plotted for three different friction coefficients 0, 0. As seen in figure, two important effects are observed as the viscous coefficient is increased. First, the final steady state velocity is decreased and second the response has less oscillation. Both of these effects could be predicted from Eq.

Additional load inertia effect: As the overall inertia of the system is increased by 0. The above results are plotted for 5 V armature input. As seen, the effect of disturbance on the speed of open loop system is like the effect of higher viscous friction and caused to decrease the steady state value of speed. Gene Mathers 0 Jack C. McCormac 1 2, William T. Segui 0 1, Richard T. Evans 0 1, Bill W. Tillery 0 1, Giorgio Rizzoni 0 1, Khurmi 1 19, Kuo — 7th Edition. Goodwin — 1st Edition. Smith, Armando B.

Corripio — 3rd Edition. Levine — 2nd Edition. Kuo — 8th Edition. Corripio, Michael Newell — 3rd Edition. Download now Automatic Control Systems. Type of file. Electronic — Hambley Allan R.