2 In the block diagram below, G(s) -1/s, P(s)P(s) s-+2 s+2 D(s)- k-oo Ше-ks[1-e-s/1001. The inverse Laplace transforms of these equations are g(t), p(t),p(t), and d(t), respectively. The parameter K scales the feedback k-0 D(s) R(s) G(s) P(s) C(s) P(s) A Consider for a moment, D(s)- 0. Simplify the block diagram in terms of G(s), P(s), P(s) and find the transfer function by substituting the equations given above B What are the zeros and poles of the system you obtained...
(30%) Consider a system with the transfer function Y(s) s+6-k (a) Determine the range of parameter k so that the system G(s) is stable. (b) Determine the value of k for which the system becomes marginally stable. (c) Assuming parameter k has the value in part(b) and hence the system is marginally stable, find a bounded input r(t) that results in unbounded output y(t). For this part, specifying the bounded input signal r(t) and a justification is enough Finding v(t)...
Consider the feedback system shown below: +e[n] xlnDelay → y[n] (a) Write an expression for y[n] in terms of xIn- 1] and y[n -1]. (b) Determine the transfer function of the system. (c) Determine the impulse response of the system (d) Determine if the system is BIBO stable.
1. Consider the family of differential equations dy/dx = y^3 + ky + k^3 . Please Help me with it, thanks so much 1. Consider the family of differential equations de set = y2 + ky + k3. (a) Are there any equilibrium solutions when k = 0? If so, what are they? (b) Draw the bifurcation diagram. That is, sketch a graph of the critical values as a function of the parameter k. Clearly label the axes. (You may...
Consider the following control system: R + Let G(s) s +23-3 and H(s) K where K is some positive constant. The transfer function H(s) can be considered a proportional feedback controller. (a) Examine the behavior of the system for different values of K. Try the values K 2, 4, 8. In each case, plot the pole-zero map of the closed-loop system and examine the step response. Comment on the stability of the system. Find the value of K for which...
Question 8 1 pts Figure 5.42 Controller Process G (s) Y(s) R(s) G(s) Block diagram for the Skills Check. Consider the block diagram of the control system shown in Figure 5.42 in Problems 8 and 9 with the loop transfer function K L(s) G,(s)G(s) s(s+10) Find the value of K so that the system provides an optimum ITAE response. OK= 1.10 K 12.56 K= 51.02 K = 104.7 Question 8 1 pts Figure 5.42 Controller Process G (s) Y(s) R(s)...
8.5 Consider a system with transfer function ĝ(s) = (s – 1)(s+2) (s + 1)(s – 2)(s +3) Is it possible to change the transfer function to S-1 8f(s) =_ (s + 2)(s +3) by state feedback? Is the resulting system BIBO stable? asymptotically stable?
. (15 points) An unstable system can be stabilized by using negative feedback with a gain K in the feedback loop. For instance, consider an unstable system with transfer function which has a pole in the right-hand s-plane, making the impulse response of the system h) grow as increases. Use negative feedback with a gain K> 0 in the feedback loop, and put H) in the forward loop. Draw a block diagram of the system. Obtain the transfer function Gus)...
Consider the unity feedback system is given below Ris) Cs) G(8) with transfer function: -K(s +1) G(S) 52 + 25 + 2 Considering that can have only positive values, the system is unstable when the value of K is ........
Consider the system described in the figure below. a. Draw a signal-flow diagram for the given system. b. Using Mason's rule find the transfer function of the system. c. Find the value(s) of K for which the system will be stable. R(S) C(s) 5+1