For a control system shown in figure below, find the value of K & Ke
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KVL and KCL
KVL stands for Kirchhoff voltage law. KVL states that the total voltage drops around the loop in any closed electric circuit is equal to the sum of total voltage drop in the same closed loop.
Sign Convention
Science and technology incorporate some ideas and techniques of their own to understand a system skilfully and easily. These techniques are called conventions. For example: Sign conventions of mirrors are used to understand the phenomenon of reflection and refraction in an easier way.
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- In the figure, the steady state error is required to be 1% for the ramp entry r (t) = 0.1 h (t) input to the system. a) Determine the type (N) number and K(OL) value of the open loop system. b) Given the input and the desired maximum steady state error, what would be the smallest value of K? c) What should Td be chosen in order to keep the system stable according to the selected K value?Given the following characteristic equation: 1+K/S(S2+2S2+8S+5)=0 (a) Using Routh method determine the range of K for which this closed loop system is stable. (b) Find the value of K for which the system has purely imaginary roots and determine the corresponding frequency of oscillations.By plotting the root locus of the system given as the open loop function : G(s)= K/(s*(s+2)); a) When K=4, show the locations of the closed loop poles on the root locus. Determine the Damping Ratio and Natural Frequency values in this gain value. b) Calculate the unit step response of this closed-loop system by calculating the Percent Overshoot, Peak, and Settlement Time values and plot them to scale. c) Scan the region on the root locus where the pairs of conjugate poles must be in order for this inspected system to work at least in the success criteria (greater than the calculated damping rate and natural frequency) in (a).
- If a=1.1 for G=1s3+6as2+11a2s+6a3 in the closed loop system in the figure, which of the following is the largest K value at which the system can be stable?The characteristic equation of control system is given as following. S3 + 6s2 + 11s + 6(1 + Kc) = 0 Determine: 1. The Value of Kc for which the control system is stable. 2. The roots of the characteristic equation for the value of Kc for which the system is on the threshold of instability.The control system G(s) = Kp / s (s+2) (s+6) has a unity feedback a. Kp is variable, discuss stability by using Routh Hurwitz method. Mark the poles ofthe system on root-locus curve below. b. When Kp = 26.7 , roots of the characteristic equation becomes s1= -0.6-1.89i, s2= -0.6+1.89i and s3= -6.8. Are you happy about this case? How do you evaluate,why ? c. How the root locus and step response would be effected by adding a controller Gc= Kp ( s + 0.5)2/ s . Give a comment about the addition of Gc on root locus andon step response.
- Ignoring the “zero” in the numerator, and based only on the denominator of the closed-looptransfer-function, determine the range of constants Kp and Ki such that the rise-time of theclosed-loop system is equal (or less than) ?r =0.18 s and so that the relative damping factor ζ isequal to (or greater than) 0.8. Use the textbook approximation for the rise-time.For the Circuit shown, Let: VCC = 3.3V R1 = 85 kΩ RE = 500 Ω R2 = 35 k Ω RC = 4k Ω β = 150 Using approximation, determine the Q-point parameters: IBQ, ICQ, and VCEQ. Indicate the exact numerical values, following the given unit.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?
- For the system shown in figure (1) with unit step input. (1) Determine the value of N when the damping ratio (=0.6)? (2) Obtain rise time, peak time, and settling time for 5% of steady state error?A first order system has a time constant of 8 s and a steady state gain of 7. Design a proportional control system such that the closed loop time constant is just 4 s. For a step in the set point of magnitude 10, what is the steady state error of this control system? Show all your working.A) Sketch the complex plane and locate poles for 2 cases: 2 Second Order underdamped systems where both systems have the same settling time, but system #1 has a larger overshoot. B) Sketch the time response for each system in part A to a unit step input. Show clearly which system is 1 and 2. Show the relative values of the overshoot for both systems, the overshoot time, damped natural frequency and time to steady state .