Common data for questions that follow: A unity feedback control system is shown below, where Ge represents the controller and G represents the plant. r(t) y(t) Gc Gp s +3 Ge(s) : s +1 K(s+2) G„(8) = The root locus is plotted by varying the gain K in the range [0, 0) 10)The shape of the root-locus, for a particular range of K, is a/an: Ellipse Rectangular Hyperbola Parabola Circle 11)lf the range of K for which the above shape is obtained is a, b] , the value of b is (rounded off to 2 decimal places): .

Common data for questions that follow: A unity feedback control system is shown below, where Ge represents the controller and G represents the plant. r(t) y(t) Gc Gp s +3 Ge(s) : s +1 K(s+2) G„(8) = The root locus is plotted by varying the gain K in the range [0, 0) 10)The shape of the root-locus, for a particular range of K, is a/an: Ellipse Rectangular Hyperbola Parabola Circle 11)lf the range of K for which the above shape is obtained is a, b] , the value of b is (rounded off to 2 decimal places): .

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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By plotting the locus-root curve of the open-loop transfer 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 ζ and the natural frequency (wn) values at this gain value. b) Calculate and scale the unit step response of this closed-loop system by calculating the %overshoot, tp and ts (percent overshoot, peak and settling times, respectively). c) In order for this supervised system to work at least in the performance criteria (computed (greater than ζ and wn)) in question (a), scan the region where the pairs of conjugate poles should be located on the root-locus curve.
In the feedback system given below; G1(s) = 5*K, G2 (s)= 1/s(s+4*4), H(s)= 1 given as time to settle down Ts ≤ 4 s and if the percent overshoot is Y*5 ≤ 5%, then what is the K value and damping ratio? For the K value you found above, the input signal r(t) is a unit step Calculate the steady state error.
3. Consider the system a) Use state feedback ? = ?? to assign the eigenvalues of ? + ?? at −0.5 ± ?0.5. Plot TT x(t) = [x1(t), x2(t)] for the open- and closed-loop system with x(0) = [−0.6, 0.4] . b) Design an identity observer with eigenvalues at −? ± ?, where ? > 0. What is the observer gain ? in this case? c) Use the state estimate ?̂ from (b) in the linear feedback control law ? = ? ?̂, where ? was found in (a). Derive the state-space description of the closed-loop system. If ? = ? ?̂ + ?, what is the transfer function between ? and ?? TT d) For ?(0) = [−0.6, 0.4] and ?̂(0)= [0, 0] , plot ?(?), ?̂ (?), ?(?), and ?(?) of the closed- loop system obtained in (c) and comment on your results. Use ? = 1, 2, 5, and 10, and comment on the effects on the system response. Remark: This exercise illustrates the deterioration of system response when state observers are used to generate the state estimate that is used in the feedback control law.
the unity negative feedback controller shown below, in whichR(s) = thetades(s) is the desired pitch angle, H(s) is the transfer function computed in part (a), and C(s) =K(s+1)/s, a proportional-integral (PI) controller with a single control gain K. (a) Suppose that you want the pitch angle to increase at a constant acceleration of 1 deg/s2. Toachieve this, you set the desired pitch angle to a parabolic function, r(t) = 0.5t2 * us(t), where us(t) is the unit step function. What is the system type n? Calculate the steady-state error ess of the closed-loop system as a function of ?(b) Compute the closed-loop transfer function, Hcl(s) = Y(s)/R(s). Write the charateristic equation of the closed-loop system in the form 1 + KL(s) =0
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).
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.
Question 1) In a dynamic system with expression [img1] in the time domain, all initial conditions are assumed to be zero. This system will be used in the standard unit feedback control system, and the reference input is unit stepfunction, the controller is a PD controller given with [img2]. Accordingly, fill in the table below. The numerical solver (Configuration Parameters under Simulation in the menu) parameters for this stage are shown above. Table 1: Design Results Exceed (%) ?? Rise time (s) ?? Sitting time (s) ?? Peak time (s) ??
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.
Figure Q2 shows the block diagram of a flight control system.a) Derive the system transfer function.b) Find out the system gain, natural frequency and damping ratio for this systembased on the standard form of second order systems.c) If K1 = 2 and K2 = 10, use the standard response sheet to find out the systemsteady-state value, overshoot and 63% rise time, with a unit step input.
Consider unity negative feedback applied to the system: G(s) = k/s(s^2+4s+5) (a) Give a complete sketch of the root locus (0 ≤ k ≤ ∞) for this system assuming a unity feedback configuration. Make sure you show all the significant features on your sketch. Give particular attention to the angle of departure from the complex poles. (b) Indicate on your root locus diagram the point at which the damping ratio of the dominant poles is 0.5.
Control System , Given transfer function, T (s) = αs + β / s^2 + (α + 2)s + β (i) Pick a pair of values for parameters α and β such that the closed-loop system is stable (ii) Pick a pair of values for parameters α and β such that the closed-loop step response exhibitszero steady-state error. (iii) Pick a pair of values for parameters α and β such that the closed-loop step response isunderdamped, exhibiting a settling time of 4/5 seconds and a peak time of π/7 seconds.
For a negative unity feedback system with the given forward transfer function:1. Evaluate the system type, Kp, Kv, and Ka.2. What is the value of the position constant?3. What is the value of the velocity constant?4. What is the value of the acceleration constant?5. What is the amount of steady-state error if the system received a parabolic function signal?