1. Obtain the rise time, peak time, maximum overshoot, and settling time for the closed- loop system given below for a unit step input. C(s)/ R(s) = s² 20 +4 s + 20
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- Consider the system below. For this question, let C (s) = K, in this question K is a positive real number. a) Prove that if the root locus of the system is drawn, the points s1,2=−0.3214 ± 2.8951j will be on the curve. (Show it by doing mathematical calculation without drawing the curve.) b) Draw the root locus of the system. c) It is desired that the dominant (= near the imaginary axis) poles of the closed loop system be at the points s1,2= −0.3214 ± 2.8951j. What should K be for this? What can be said about the stability of the closed loop system for this K value? d) What are the unit step, ramp and parabolic reference tracking errors of the system for K in the option c?33 Determine the natural angular frequency, the damping factor, the rise time, percentage overshoot and 2% settling time for systems with the following transfer functions: (a) 100/(s + 4s + 100), (b) 49/(s + 4s + 49). * Note (that the question relates to control system)G(s)=((s+1)*(s+15))/((s+0.1)*(s+2.5)*(s+120)*(s+240)) 1-draw nyquist 2- Nyquist criterion, compute the number of unstable poles of the closed loop system as a function of K 3-determine for which values of K the closed system is stable.
- Referring to the unity-feedback control system defined by: A. Find the following requirements in plotting the root locus. number of branches number of asymptotes asymptote real-axis intercept asymptote line angles real-axis break-away points / break-in points points at the jw-crossing B. Manually plot the root locus based on the requirements from item A C. Create a Matlab m-file to verify your root locus plot. Write down the Matlab code belowThe closed loop pitch rate control of an airplane operating at a certain altitude and sound speed is shown in the following blog diagram as a representation. Features expected from this system ωIt is known that n>2 and ζ≥0.15. Accordingly, G Assuming c(s)=K, find the K value corresponding to the maximum ζ value that can be used by plotting the root-locus curve of this system. It should be taken into account that the system should be stable.System Dynamics and Control The characteristic equation of a closed loop system is: s5+s4+2s3+s2+20s+12s5+s4+2s3+s2+20s+12 Use Routh-Hurwitz criteria and determine if the system is stable or not. Complete the Routh array; show all steps of your solution and determine the number of stable and unstable roots.
- What is the input to the system with specification given, Kp = 10, 500? A. Step function B. Ramp Function C. Parabolic FunctionOne of the most important characteristics of control systems is their transient response Select one: a. Only for underdamped systems b. Only for zero damped systems c. True d. Only for overdamped systems e. FalseExpress the following signal in terms of the unit ramp function, ur(n).
- Set up a system of first-order differential equations for theindicated currents I1 and I2 in the electrical circuit ofFig. 4.1.14, which shows an inductor, two resistors, anda generator which supplies an alternating voltage drop ofE(t) = 100 sin 60t V in the direction of the current I1.Elaborate this sentence : The maximum settling time of the DAC is usually determined by its MSB settlingA coil, resistor, and capacitor are in parallel. The resistance is 1 Ω; the capacitive susceptance is 1.0 siemens; the inductive susceptance is -1.0 siemens. Then the frequency is cut to half its former value. What will be the admittance vector, G + jB, at the new frequency? Provide illustration of the circuit.