Figure dlagral unity-feedback control system Proportional Controller Plant R(s) C(s) s(3s +1) K 5+2s +4
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- 2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2Q5) For unity feedback control system with forward transfer function (G(s) ): G(s) = ; By using root locus graph calculate the value K(s+5) (s+2)(s²+12s+50) of gain (K) which must be added to get the dominant root at damping ratio (-0.886) and natural frequency (w = 8 rad/sec )? www CTRICAL ENGINFor the system with open loop transfer function given by R(s) K s(s + 1) (s² + 4s +13) where K is the feedback gain. Sketch the root locus a) How many asymptotes are there for this system's root locus? what are asymptote angles? What is the center of asymptotes? C(s) b) Does the root locus cross the imaginary axis? where and what is the value of K at that point? c) Is there any break away, break in points? What is the approximate values of these points?
- P6. The open loop transfer function of a unity feedback system is K(s+2) G (s) = s(s+3)(s²+2s+10) 1- Find the value of K so that the error steady state for the unit ramp input r(t)=t is less than or equal to 0.01. 2-For the value of K found in part (1), use the Routh method to verify whether the closed loop system is stable.The Routh-Hurwitz criterion to be used to determine the stability of a system with a characteristic equation given by 85 + 2s4 + 2s3 + 4s² + 11s + 10 Comment on the stability of the system. Neutral Stable Unstableand 1) 2) LIUS S Consider the following feedback system, where K is a constant gain G(s) === 1 s3 +382 +s+1 Let K be a real number. Utilize the Routh-Hurwitz criterion to derive stability conditions for the closed-loop system. Suppose that the reference input r(t) = 1. What are the steady-state tracking errors (ess) for K = 1 and K = 3, respectively? R K G(s) Y Figure 2: Control system in Problem 2.
- P6. The open loop transfer function of a unity feedback system is K(s+2) G(s) = s(s+3) (s²+2s+10) 1- Find the value of K so that the error steady state for the unit ramp input r(t)=t is less than or equal to 0.01.1) Consider the system below: Vehicle Controller Steering dynamics Desired Actual bearing angle bearing angle 50 1 K s2 + 10s + 50 s(s + 5) Figure 1: Simplified Block Diagram of a Self-Guiding Vehicle's Bearing Angle Control. • Find a K value that the system has minimum rise time and minimum overshoot. Let us call this proportional gain as Kopt Show each step while finding Kopt- Show the necessary graphical solutions. Simulate the system response with 3 different K values. (Kopt and two other K values close to Kopt) Show the system response (actual bearing angle) in a single graph for different K values. • Comment on the results.b. Use Routh - Hurwitz stability criterion to determine the system having the following function is stable. s 3+ 3s?+ 7s +k = 0
- For the given close-loop system transfer function, determine its stability using Routh-Hurwitz Test for Stability.1. What is the stability of the system? (Stable, Unstable, Marginally Stable)For the feedback control system has: G(s)=- s(s+2)(s+4) H(s)=D s +2s +5 Investigate the stability of the system using Routh Criterion method.s)- Characteristic equation for a 5th order system is given as: s5 + 4s4 + 3s3 + s? + 2s + 10 Using Routh-Hurwiz stability criteria, determine if the system is stable or unstable (show your work)