Unit step input

Generalized second-order system response to a unit step input... 

Consider a second-order system whose steady-state gain is K, undamped natural frequency is Wn and whose damping ratio is (, where C < 1 For a unit step input, the block diagram is as shown in Figure 3.18. From Figure 3.18... 

The generalized seeond-order system response to a unit step input is shown in Figure 3.19 for the eondition K = 1 (see also Appendix 1, sec ord.m). 

When a unity gain seeond-order system is subjeet to a unit step input, its transient response eontains a first overshoot of 77%, oeeurring after 32.5 ms has elapsed. Find... 

If the sampling time is one seeond and the system is subjeet to a unit step input funetion, determine the diserete time response. (N.B. normally, a zero-order hold would be ineluded, but, in the interest of simplieity, has been omitted.) Now... 

For the spring-mass-damper system given in Example 8.6, evaluate the transient response of the state variables to a unit step input using... 

For the case with a unit step input such that X = 1/s, we have, after partial fraction expansion,... 

Find the outputs X2, T,) of the two systems of Example 18.7 for a unit step input in m, . Use partial fractions expansion and long division. 

General Second-Order Element Figure 8-3 illustrates the fact that closed-loop systems can exhibit oscillatory behavior. A general second-order transfer function that can exhibit oscillatory behavior is important for the study of automatic control systems. Such a transfer function is given in Fig. 8-15. For a unit step input, the transient responses shown in Fig. 8-16 result. As can be seen, when t, < 1, the response oscillates and when t, < 1, the response is S-shaped. Few open-loop chemical processes exhibit an oscillating response most exhibit an S-shaped step response. 

The response has been plotted in Figure 11.1a for various values of C, > 1. It is known as overdamped response and resembles a little the response of a first-order system to a unit step input. But when compared to a first-order response we notice that the system initially delays to respond and then its response is rather sluggish. It becomes more sluggish as increases (i.e., as the system becomes more heavily over-... 

Use Laplace transforms and find the dynamic response of the following linearized systems to unit step input changes. 

Figure 29.8 (a) First-order lag without hold element (b) its discrete-time response to unit step input. 

Before we proceed to examine the physical origin of second- and higher-order systems, let us analyze the dynamic response of a second-order system to a unit step input. Such analysis will provide us with all the fundamental dynamic features of a second-order system. 

III.28 Sketch, qualitatively, the response of systems with the following transfer functions. Assume unit step input changes. 

III-61 For each of the systems with transfer functions given below, (a) draw the corresponding block diagram, (b) identify the poles and zeros of the transfer function, (c) plot the response to a unit step input change, and determine the ultimate response to a sinusoidal input sin 21. 

Figure 29.7 Sampled-value response to unit step inputs of (a) pure integrator (b) first-order lag.

Then the St6p command is used to calculate the response of y (73) to a unit step input in the first input (To) by specifying iu = ]. 

Find y nT.n for a unit step input in U(,) for the system in part (a) of Problem 14.2 by partial-fractions expansion and by long division. Use the following numerical values of parameters ... 

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