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5. 8.) Find the ranges of K for which the systems shown below are stable using...
2. (8 pts) A system has a characteristic equation s3 Ks2 ( K)s6 0. Using the Routh- Hurwitz criterion, determine the range of K for a stable system.
control systems
1) Using Routh Hurwitz Stability Criteria, determine whether the following system of equation is stable or not. a) S4+253+3S2+45+5=0 2) Using the Routh Hurwitz stability criterion, determine the range of K for stability of the following characteristic equation. a) s4+2s8+(4+K)s2+9s+25=0 3)Sketch the root-locus of the following systems a) G(s)H(s) = s(s+1)(s+2) b) G(s)H(s) = 52(8+3.6) K(5+1)
Determine if the following systems are stable or unstable and find the range of K using the Routh-Hurwitz criterion
G(s).H(s)= k.(s^2-4^s+8)/(s3+15s+50s) used Root locus by hand and find K for system to be stable. used Routh-Hurwitz stability by hand and find K for system to be stable.
3. For the feedback control system shown in Figure Q3 below, the forward-path transfer function given by G(s) and the sensor transfer function is given by H(s). R(s) C(s) G(s) H(s) Figure Q3 It is known that G(s) -- K(+20) S(+5) H(s) = and K is the proportional gain. (S+10) i. Determine the closed-loop transfer function and hence the characteristic equation of the system. [6 marks] ii. Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system. Determine the...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
Consider the system shown in Figure 1. Using the Routh-Hurwitz Criterion, determine the range of K for which the system is stable. R(s) Figure 1
Question 2 System Stability in the s-Domain and in the Frequency Domain: Bode Plots, Root Locus Plots and Routh- Hurwitz Criterion ofStability A unit feedback control system is to be stabilized using a Proportional Controller, as shown in Figure Q2.1. Proportional Controller Process The process transfer function is described as follows: Y(s) G(s) s2 +4s 100 s3 +4s2 5s 2 Figure Q2.1 Your task is to investigate the stability of the closed loop system using s-domain analysis by finding: a)...
8. The input r(t) and output y(t) of a transfer function block are sin(wt) and A sin(at +) respectively and ti are shown in the following figure. Determine the most suitable values for A and . a. A = 1.67 and $ = 45° b. A = 1.67 and $ = -45° C. A = 0.6 and $ = 45° d. A = 0.6 and 6 = -45° 9. Routh criterion is applied to check the stability of polynomials +s...
For the unity feedback system with forward loop T.F. G(s) =s(s+2)(s+4) Find, using Routh criterion, the value of K for which the system has undamped oscillatory response. A unity feedback control system has the following open-loop T.F k1 s(s+1)00.5s +1) And an input of r(t) 5t b) It is desired that, for a ramp input, Ess 0.1. What minimum value must ki have for this condition to be satisfied? cFor the value of ki determine in part (b) is the...