9) Consider the system defined by i = Ax + Bu where 1 A = 1 ; В — -5 -6 By using the state feedback control u = -Kx, it is desired to have the closed loop poles at s = -1± j2, s = -10. The state feedback gain matrix K is K = [25 20 9] K = [45 30 8] K = [40 25 10] K = [49 20 6]
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- When a unit ramp input is applied to the unity feedback system having closed loop transfer function, C(s)/R(s)= Ks+b/s2+as+b , (a>0, b>0, K>0), the steady state error will be ?The forward transfer function G(s) with a H(s) feedback configuration of an uncompensated Basic Satellite Launching System is as shown in figures 1 and 2. A- Write a m-script and generate the time and frequency response of the system shown in Figure 1. (a = 4, b = 2, c=2, d = 1and e=10, and f=4). B- Compute the percent overshoot, peak time and settling time, using second order approximation through pole zero cancellation and unity feedback configuration shown in figure 2.The forward transfer function G(s) with a H(s) feedback configuration of an uncompensated Basic Satellite Launching System is as shown in figures 1 and 2. A- in the picture B- Compute the percent overshoot, peak time and settling time, using second order approximation through pole zero cancellation and unity feedback configuration shown in figure 2. C- Summarise the results (a) and (b) in tabular form and comment on the stability of both systems based on time response graph for (a) and computed values in (b).
- The margins of stability for K = 12 of the unit feedback system shown in the figure are given below. Phase crossover frequency : Wfc = 2rad/s Gain crossover frequency: wgc = 1.4rad/s Phase Margin = 16.8 degree Amplitude Margin Kg = 6dB (NOTE: Use 3 decimal places in your operations.) a) Calculate the amplitude margin for K 60. b) Calculate the point where the KG(jw) Nyquist Diagram intersects the negative real axis for K 60.are given a system’s transfer function as T(s) = 21 Construct a state-space model for the given system using ” Observer Canonical Form” method. | that the full state information of this system is available, design a state-feedback controller for this put the desired closed loop poles at ~2+ 2. Now, assume that the state information of the system are measurable, for this case what kind of controller do you suggest? Design this controller so that the ¢ Joop poles of the system are located at —10 + 510.Consider unity FBCS (feedback contrpl system) whose open loop transfer function is given by G(s)= 0.4+1/s(s+0.6) , Obtain the response to stop i/p. For the same calculate rise time Tr, peak overshoot Mp, peak time Tp and setting time Ts?
- A Unity feedback control systemG(s)10/((s+1)(s+3)(s+20)) and Gc(s)=21(s+1).A)what is the settling time, percentag eovershoot and time to first peak?B) given gain and phase margin and sketch bode plot ?A unity feedback system has a forward transfer function given below. Find the value of K to yield a static error constant of 25,000. 18922.17 18992.17 18292.17 18229.17Sketch the root locus for unity feedback system with following forward gain function: KG(S) = K(S+1)(S2+2)/S2-9 For what range of K is system stable & unstable.
- Consider the feedback system given the open loop transfer function below G(s)H(s) = K / ( S (s+3) (s+2)) a) Using the Routh-Hurwitz criterion, for which value of K, the poles of the closed-loop system take the pure imaginary value.b) What will be the maximum value of K for the system to be stable?c) Calculate the value of K, where the real value of the complex root of the system is Re{s}=-1. Tip 1: Closed loop transfer function T(s) = G(s) / ( 1+ G(s)H(s)) .Routh HurwitzIn order to perform the criterion analysis, the denominator of the closed-loop function will be examined. Tip 2: The real value of the system complex root Re{s}=-1 is expressed by the following formula f^2(s) = p(s-1) p(s) is the payoff of the closed-loop function.A unity-feedback system has forward transfer function (see attached). a) Sketch the root locus for this system as K varies from 0 to ∞; b) Use the Routh-Hurwitz test to determine the range of K for the system to be stable; show this value of K on the root locus plot.A unity feedback system has loop transfer function: L(s) = Gc(s)G(s) = 4(s+z)/s(s+1)(s+3) a) Draw root locus as z varries from 0 to100 b) using root locus, estimate the percentage overshoot and settling time (within 2%) of system at z =4 c) determine actual overshoot and settling time at z = 4