7. Carombayenin For the closed loop system, find the (1) The range of values of K for stability (2) The value of K such that the maximum overshoot is 5% with a rise time of less than 1.3 s G(s) = K(s + 2) s² + 2s + 3 H(s) = 1
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- Q5 Hydraulic power actuators were used to drive the dinosaurs of the movie Jurassic Park. The motions of the large monsters required high-power actuators requiring 1200 watts. One specific limb motion has dynamics represented by: y = [0 1] Design the state feedback gain matrix using the Ackermann's formula method. Where the new closed loop poles to be placed at s1,2 =-17j3.2. Consider the closed-loop system shown below. Determine the range of K for stability. Assume that K > 0. R(s) K S-2 (s + 1)(s² + 6s+25) C(s)b. Use Routh - Hurwitz stability criterion to determine the system having the following function is stable. s 3+ 3s?+ 7s +k = 0
- 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)Q(s) = S5 + 2S4 + 2S3 + 4S2 + 11S + 10 = 0 i). Identify the stability of the system using Routh Hurwitz Algorithm. (ii). Comment about the Roots location.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.2
- Problem-3. Consider the closed loop transfer function from R(s) to C(s) as given below as given below. 85 H(s) = (s+5)(s? + 2s +17) MATLAB gives the partial fraction values of the Laplace transform C(s) to the unit step input as follows: Num: Denom: -0.5313 -5.0000 -0.2344 + 0.3906i -1.0000 + 4.0000i -0.2344 - 0.3906i -1.0000 - 4.0000i 1.0000 d) Find the overshoot and peak time by using the reduced-order transfer function Hint:Tp = e-(n{//1-§2 %OV = Wn V1- 2)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 Unstable(c) An electronic Pl temperature controller has an output p of 15 mA when the set point equals the nominal process temperature. The controller response to step change in the temperature set point of 3 mA is shown below. t(s) 0- 0+ 20 60 80 Determine the controller gain K, and the integral time.r p (mA) 8,0 6,8 6.0 4.4 3.6
- For the unit step response shown find the transfer function of the system. 1.4 1.2 1.O 0.8 0.6 0.4 0.2 10 15 20 25 Time (seconds) RespanseProblem 1. For the systems (s + 2)² 1. G₁(s) = (s+1)(s² + 1)' (s+1)(s+2) 2. G2(s) = (s - 1)(s - 2)(s - 3)' => (a) Using the root-locus rules, draw the root locus plot by hand.1 Problem 5 4 State, x(t) SAWNO-Nw. ● ● Case 1 O 2 6 Time, sec. underdamped critically damped State, x(t) • overdamped 54321 ONS TY Case 2 2 ▷ Time, sec. 8 10 State, x(t) 5 2 + 3 4 Case 3 2 ▷ 6 Time, sec. 5432 State, x(t) & A & No. 2 Match each of the resposes above to one of the following second-order system types: • undamped Case 4 ▷ Time, sec.