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For the unity feedback system of Figure P8.3, where
sketch the root locus and find the range of K such that there will be only two right-half-plane poles for the closed-loop system. [Section: 8.5]
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Control Systems Engineering
- For 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?arrow_forwardHomework: For a unity feedback system with the forward transfer function: K(s + 20) G(s) = s(s + 2)(s+3) find the range of K to make the system stable.arrow_forward5. A feedback system's open-loop transfer function is K G(s) = s(s+ 3)(s+ 6) 1)Sketch the system root locus. 2)Find the range of K when the system is a stable system.arrow_forward
- The open loop transfer function of a humanoid's arm control system is given as: K G(s) = 2 s(s + 2s + 2) (a) Clearly locate all poles and zeros on a linear graph paper. Provide calculations for the following: asymptote angles, centroid for asymptotes, and departure angle from complex pole. (b) Plot the complete root locus, with the locus on the real axis is clearly shown. Use the scale of 4 cm : 1 unit for both axes and choose the longer side of the graph paper as the real axis.arrow_forwardblock diagram pls solve fast As Simplify the multiple loop feedback control system? R(s) G₁ G₂ H3 H₂ + G3 H₁ G₁ Y(s)arrow_forwardGiven the system equipped with unitary feedback, whose direct branch transfer function is: Design a PID controller with one of the Ziegler-Nichols methods.arrow_forward
- Figure Q2 shows the block diagram of a unity-feedback control system Proportional Controller Plant R(s) C(s). s(3s +1) 5+2s² +4 K 2.1- Determine the characteristic equation. 2.2- Using the Routh-Hurwitz criterion to determine the range of gain, K to ensure stability and marginally stability in the unity feedback syste m.arrow_forwardGiven the system equipped with unitary feedback, whose direct branch transfer function is: (s + 4) (s + 2) (s+5)(s + 9) Design a PID controller with one of the Ziegler-Nichols methods. G(s)=arrow_forwardWe consider a dynamical system represented by the block diagram: Simple negative feedback: U(s) E(s) input, + with T₁(s) = T₂(s) = 3 + T,(s) 1 S T₂(s) a s²(1+s) X(S) output measurement with a 4 and Calculate the open-loop transfer function at s=6.arrow_forward
- QUESTION 5 An open-loop transfer function for a root locus is given as: 2K (S + 4) S(S + 2) (S + 8) Use the given transfer function to determine the following: 5.1 The open-loop poles and the zeros G(s)H(s) = Do some of the loci break away? Explain. The centre of asymptotes The asymptotic angles 5.5 The stability of the system 5.2 5.3 5.4arrow_forwardA Block diagram of a feedback control system is shown in Figure Q3. Using the Block Diagram Reduction Method, solve for the output Y(s) when:(i) Input D(s) = 0,(ii) Input R(s) = 0,(iii) Input R(s) and D(s) are both applied (i.e., R(s) ≠ 0 , D(s) ≠ 0).arrow_forwardFor 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)arrow_forward
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