J ror sy stein is given by K(s + 2) G(s) =+7) For K > 6, che scability characteristic of the open-loop and closed-loop configuration of the system are, respectively: Stable and stable O Unstable and stable O Unstable and Unstable 口 Stable and Unstable
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- A plant of transfer function G(s) is to be operated in closed-loop, with unity negative feedback, and a controller in the forward path as shown in Figure Q4 R E controller G(s) Figure Q4 (a) Discuss the main steps of generating the root-locus plot for the closed-loop system of Figure Q4 (b) If the controller is a simple gain factor K, produce an estimated root-locus plot for the system with G(s) = S+8 (s+4)(s+6)(S-1)First order control system and response closed loop feedback control first order system with the a Suppose a plant in system is modelled as a transfer function defined below: Gar (s) ((s)/R(s) (5+2) / (5+5) @Sketch the control system diagram showing the input signal r(t), controller Gr(s), plant Gr (s), output signal CHY and unity feedback. Sketch the zero-pole diagram of the system. Ⓒ find the output response c(t) 의 step input ult) is applied to the system... he system if 16 a unit Ⓒ Which component of the system response c(t) is the forced response for the steady state and which part the natural response (or transient state). ⒸFind the sampling frequency and period that must be selected for this system to meet a sensor delay of 0.025s)) The Nyquist Plot of a system G(s) = in a unity feedback loop (Figure 3) is shown in Figure (s+1)² 4 for K = 1: a). Is the closed-loop system stable for K = 1? Justify your conclusion with Nyquist Stability Criterion ? b). Discuss the impact of the value of K, increasing or decreasing, on the closed-loop system stability and find the critical value of K in Nyquist Plot. Applying Routh-Hurwitz Criterion to validate your conclusions. R(s) + Y(s) G(s) Figure 3: Nyquist Diagram 15- 05 Real Asis
- Q2) Consider the following feedback system outlined in Figure Q2 Plant R(s) 10 C(s) S+1 Figure Q2 a) Derive the closed loop transfer function GRe(s). b) Calculate the value of Ky that will result in the closed loop system to have a maximum overshoot of 35% and a peak time of approximately 1 second. c) For the following systems assume zero initial conditions. Determine i) The peak overshoots. ii) Corresponding peak times iii) Decay rate characteristics. Produce a sketch of the unit step response using the above values calculated. vate ettQ8 Figure Q8 shows a plant of transfer function G(s) to be operated in closed-loop, with unity negative feedback, where the controller is a simple gain factor K-4, and G(s)-- R E 2 s²+7s+2 controller U. G(s) Figure Q8 (a) Obtain poles of this closed-loop system and determine if this system is stable. (b) Use Routh test to determine range of the controller gain factor K values that would make this closed loop system stable. (c) Formulate Nyquist stability criterion and discuss how this criterion can be used to determine stability of the closed-loop system shown in Figure Q8(a) Consider following differential equation. d³y d²y +3. dt3 dy d³x d²x dx +6 + 8x dt +5 +y = +4 dt² dt dt3 dt2 Y(s) i) Find the transfer function of X(s)' ii) Consider that the system in i) has a unity feedback. For this system identify parameters below. 1) Open loop transfer function 2) Open loop poles 3) Open loop zeros 4) Real axis segment 5) Break away or break in point 6) Sketch of the root locus
- Q3- Sketch the root locus of a unity feedback linear time invariant K(s2-7s+7) for (2s+6s²+4s) control system of open loop transfer function: positive values of loop gain and damping ratio 0.56.Topic: Feedback and Control System Block Diagram Algebra and Transfer Functions of SystemWill leave a like if the answer is correct, please check the instructions carefully, thanks!Figure Q2 shows the block diagram of a unity-feedback control system 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. R(s) + C(s) K (6s+2) 3+25+ 4 1/2
- Q2) Consider the following feedback system outlined in Figure Q2 Plant R(s) + 10 1 C(s) S+ 1 K, Figure Q2 a) Derive the closed loop transfer function GRC (S). b} Calculate the value of Ky that will result in the closed loop system to have a maximum overshoot of 35% and a peak time of approximately 1 second. c) For the following systems assume zero initial conditions. Determine i) The peak overshoots. ii) Corresponding peak times iii) Decay rate characteristics. Produce a sketch of the unit step response using the above values calculated.Explain how the Nyquist stability criterion can be used to determine the stability of a closed-loop feedback system. Formulate the criterion for a system with no right-half plane open-loop poles. (a) (b) Consider the Nyquist plot of the frequency response of the system G(jw) = 500 shown in Figure Q4 below. (jw+1)(jw+10)² i. Explain how the gain margin can be obtained from the Nyquist plot and determine its approximate value from Figure Q4. What is the maximum value of an additional gain K for which the closed loop would still be stable? 0.5 -0.5 -0.5 0.5 Real Axis Figure Q4 i. Explain how the phase margin can be obtained from the Nyquist plot and determine its approximate value from Figure Q4. Assuming that the corresponding point on the plot occurs at 4rad/s, what is the maximum delay which can be added to the system before the closed loop would become unstable? Sketch the approximate Bode diagram for the system in part (b) of the question, clearly showing the asymptotes and corner…Design the state feedback controller so that G(s) is %OS=10% of the system and the settling time Ts=1 sec when given as follows. The real value of the third pole is made to be five times the real value of the dominant pole. (Don't use MATLAB and solve it.)