5. Given the following closed-loop system transfer function (20 points) s2 + (1 + 0.1k)s +...
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+200) G(s) = Do the following using Matlab: a) Sketch the root locus. b) Find the range of gain, K that makes the system stable c) Find the value of K that yields a damping ratio of 0.707 for the system's closed-loop dominant poles. d) Obtain Ts, Tp, %OS for the closed loop system in part c). e) Find the value of K that yields...
2. Consider the closed-loop system shown below
Here Kp represents the gain of a proportional controller, and
the process transfer function is given by
.
(a) Sketch the locus of the closed-loop poles as the
proportional gain, Kp, varies from 0 to ∞. Be sure to clearly mark
poles, zeros, asymptotes, angles of arrival/departure,
break-in/away points, and real axis portion of the locus.
(b) Using Routh's array, determine the range of the proportional
gain, Kp, for which the closed-loop system...
muibliam 5(20%). The closed-loop system is given below. Controller (a) (S%) Find the system transfer function and discuss the range of Ko to make the eystom stuibie assuming K (t)(S%) Find the percentage of overshoot and stendy state error to the unit ramp input as a function of your design parameter Ke assuming K4 ( d) 5%) Find hed sagn parameters Ko and Kr such that the damping ratio of the closed- lonp system is O15 and the steady state...
please solve
If a system has the open-loop transfer function G(s) s(s+25n) with unity feedback, then the closed-loop transfer function is given b T(s) s2+20ns+wf Verify the values of the PM shown in Fig. 6.36 for = 0.1,0.4, and 0.7. Figure 6.36 Damping ratio versus 1.0 0.8 PM 2 0.6 0,4 0.2 0 0° 10° 20° 30° 40° 50 60° 70° 80° Phase margin Damping ratio,
If a system has the open-loop transfer function G(s) s(s+25n) with unity feedback, then...
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...
blem 5 (2000): The closed-loop system is given below. Controller El(s) ) (5% o) Find the system transfer function and discuss the range of Ko to make the stem stable assuming Kp-5. ) (5 %) Find the percentage of overshoot and steady state error to the unit ramp input as function of your design parameter Kp assuming KD-4. :) (5%) Find the design parameters KD and Kp such that the damping ratio of the closed- pop system is 0.5 and...
F(G) = list 62 Transfer function: F(s) = K, s + K2 with closed loop 54 + 5g3+ 45²-10s control system a) H(s) = + F(s) 5(5-1)(8+3+;)(5+3) Find the range of gains in the K, , Kz plane for which closed loop system is stable. And sketch the result. b With K,K, K₂=0.1K, sketch the root locus for system of part (a). Show topen loop poles and zeros, asymptotes of loci fork loci segments on real axis and imaginary axis...
A unity feedback system is shown in Fig. 1. The closed-loop
transfer function ?(?) of this system is given as
?(?)=?1?4+2?3+(?2+1)?2+?2?+?1.
a) (20%) Using Routh-Hurwitz criteria, find expression (in
terms of ?1 and ?2) and range of value of ?1 and ?2 such that the
above system is stable.
b) (4%) It is desired to achieve steady-state error of less
than 0.3 with a unit ramp input. Find an additional constrain in
terms of ?1 and ?2 such that the...
Problem #4: Applying Routh's Criterion, use the following transfer function to compute the closed-loop system from applying a unity feedback. K(s +4) Gis)- NS D(s) (s+0.4s+4)(s+1)s + 0.5)] a) Find the range of K that makes the system stable? Show your work. You are free to use MATLAB to help with the computation to get to your end results.
Q2. Fig Q2 shows the block diagram of an unstable system with transfer function G(s) - under the control of a lead compensator (a) Using the Routh's stability criterion, determine the conditions on k and a so that the closed-loop system is stable, and sketch the region on the (k, a)- plane where the conditions are satisfied. Hence, determine the minimum value of k for the lead compensator to be a feasible stabilizing controller. (10 marks) (b) Suppose α-2. Given...