Given a unity feedback system with G(s) = 12 s(8+5)* A proportional controller Kp is inserted before G. Find the roots of the characteristic equation that would yield a damping ratio of 0.5 for the closed-loop system. Roots = What is the value of Kp that would yield these roots? Answer: tj What is the percent overshoot at this damping ratio? Answer:
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- Homework2:)A feedback system employing output rate damping is shown in Figure below. A. Find the values of K1 and K2 so that the closed-loop system resembles a second- order system with damping ratio equal to 0.5 and frequency of damped oscillations 9.5 rad/sec. B. With the above values of K1 and K2, find the percentage overshoot when input is step input. C. What is the settling time for 2 percent tolerance? 14 Scanned with CamScanner Computer Technology Eng. Dept. Control Engineering Fundamentals Third Class R(s) > Ki C(s) sCI+s) Answer: K=120.34 K2-9.97 Mp=16.31% t=0.729 secA unity feedback system has the characteristic equation shown below. For some gain K the unity feedback system enters into a state of self-sustained oscillations. Use the Routh - Hurwitz Stability Criterion to find the frequency of this self-sustained oscillation in rad/ sec. Enter your answer in decimal form to two decimal places. 4 + 65³ +12s² + 10s + (3+K)A feedback system root locus graph shown in figure below. For damped frequency 8.04 Hz, the gain K = 10 Imaginary Axis (seconds) ÖAN÷O-NWAGALBE -10 -20 -18 -16 Root Locus -14 -12 -10 -8 -6 -4 Real Axis (seconds) Ņ 0
- Chose True or False * True False If a system is subjected to step input, the type of static error coefficient performs the function of controlling steady state error is position. If a type 1 system is subjected to parabolic input, the value of steady state error will be zero . The elements of rotational motion are the Mass, Spring, Friction. the notation represents the feedback path in closed loop system is c(t). The output signal is fed back at the input side from the Summing point. In an integral controller the output is proportional to integral of input. Two loops are said to be non- touching only if no common Branch exists between them. In block diagram representation, the lines connecting the blocks, known as branches. Order of the system can be determined from the e forward path transfer function of the system. A system with transfer function 1/Ts+1, subjected to a unit step input to reach 63.2% of final value, The value of t is T/2.how to find the closed loop poles and zeros on a tf like this by hand. With unity feedback.Given the feedback circuit below and assuming the voltage amplifier has gain A₂, input resistance R₁ and output resistance Ro, answer the following questions: + a. Loop gain b. Closed loop gain Re C. Input resistance d. Output resistance Rin м + RE A) Sketch the feedback small signal model of this circuit. (Hint: You may convert the input VIN and source resistance Rs to its Norton current equivalent if needed) B) Find the following in terms of the amplifier parameters and resistances R, and RF: Rout
- Consider a closed-loop system in the standard negative unity feedback configuration with controller C(s) and plant G(s) in the forward path. R(s) C(s) = G(s) If you use Pl, control, i.e. C(s) = Kp + and the plant is given by G(s) = 1 what must the proportional gain K, be to achieve a closed-loop damping ratio < = 0.1 and natural frequency wn = 10 rad/s? Kps+K; Y(s)For the given four statements below, which of the following are not correct about an op-amp with negative feedback arrangement? i. Negative feedback reduces the gain of the op-amp circuit to desired value. ii. Negative feedback takes portion of the output and applies it back in-phase with the input. iii. Negative feedback controls the voltage transfer characteristic of the op-amp circuit. iv. Negative feedback maintains the oscillations. i and ii O i and iv iii and iv O i and iiiQ8 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
- Q2: For the unity feedback second order system shown below, if R(s) is a unit step, trace R(s), E(s) and C(s). Take a. K=50 and kl=10 b. K=k1=10 c. K=25 and kl=10. Comment on the results in each case. R(s) E(s) K. C(s) (s +. kl)sA 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)3. Inverting Amplifier is a normal OP-Amp in which the output is given as feedback with a feedback resistor. i. Draw a circuit diagram for the inverting amplifier. Derived the expression for the closed loop gain for the inverting amplifier. iii. In an inverting amplifier input resistance (R1) =2.2 k2 and feedback resistance 220kN. Calculate the closed loop gain for the inverting amplifier.