01: Consider the closed loop system that shown in Fig.(1):KR(s)Cis)s(Ts+1)H(s)Fig.(1)The output time response (with unit step input) for this system (if H(s)=1) is givenby the following equation:C(1) =1-e 0454sin(1.045t + 0)0.9165a) Determine the value of natural frequency and damping ratio for this system.b) Find the value of K and T for this system.c) What is the value of the angle (0) in this system.d) Prove that the C(1) at 1=1, reach nearly to the desired value.Q2: Using the Routh's criterion, determine the stability of the closed-loop system that hasthe following characteristic equation:s6 + 255 + 5s* + 853 + 852 + 8S + 4 = 003: For system shown in Fig.(2) below:11R(s)+C(s)s+10hFig. (2)What is the value of h that make the ess (at t = 10)= 0.01 for closed loop response if the pis unit ramp.

NECESSARY CONDITIONS FOR STABILITY: All the coefficients of the Characteristics equation are…

Answered: 01: Consider the closed loop system…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Measurements conducted on a servomechanism show the system response to be: C (t) = 0.3 e 60t + 1.5 e 10t, when subjected to a unit step input. [1].Obtain the expression for the closed-loop transfer function. [2].Determine the undamped natural frequency and damping ratio of the system.
A car was ignited & a signal from the engine i.e a(z) was passed through a cascade of 2 passive RC lowpass filters to generate an output signal, b(z).a.Show a differential equation derivation to describe the systemb.Make a sketch utilizing circuit diagramc.Mention if the RC system in question above isi.Time in-variant / Time variant ii.Non linear / lineariii.Non-invertible / Invertibleiv. Non-causal / Causal v. Have no memory / Have memory sytems.d. d2b(z)/dz2 + 3(db(z)/dz) +2b(z) = 3(da(z)/dz) +2a(z)Let's assume that the d.e(differential equation) above is that which is characterised by the RC system in the main question above.Where a(z) & b(z) is the input & output of the RC system respectively.Considering an impulse of a(z)=δ(z) is applied to the system, determine the output b(z) of the system
The transfer function is H(s) = (1.2s+0.18)/(s3 + 0.74s2 + 0.92s) and C(s) = (K(s+1))/ s A) A disturbance input W(s) =W/sk , where W is a constant, into the feedbackcontroller as shown below. We set R(s) = 0. What type of disturbance input W(s)(step, ramp, or parabola) can thesystem reject (i.e., the steady-state error ess is a nonzero constant)? (B) Suppose you want to design the controller C(s) to produce a closed-loop response to areference step input that has no more than 30% maximum overshoot (Mp ≤ 0.30) and a peak timeof no more than 8 sec (tp ≤ 8). Given the specifications on Mp and tp , compute the constraintson the damping ratio ζ and the damped natural frequency ω, assuming that the closed-loop systemis approximated as a 2nd-order underdamped system. Sketch the allowable regions in thecomplex plane (the s-plane) that these constraints define, and shade in the regions where the polesshould not be placed.
Consider a unity feedback system with G(s) = K (s+3)/(((s+7)^2+3^2)*(s+4)). Find the angle of departure of the root locus from the complex pole containing the positive imaginary part. Express the angle in radians in [-pi,+pi] and degrees in [-180,+180]. Sketch the root locus accurately
Examine the closed loop stability of a system whose open-loop transfer function is given by.G(s) H(s) =1+4s/s^2(1+s )(1+2s) use nyquist plot
Open loop transfer function G(s) = K/ s(s+3)(s+4) for a system with a) Using the Routh Hurwitz criterion, the poles of the closed-loop system are only purely imaginary. Calculate the value of K for it to have roots on the axis. b) Calculate the maximum value of K for the system to be stable. c) Calculate the values of K for the system to have roots at the value of -1 on the real axis.
For the system shown in the attached image, assume A = 1300 and n = 860. Draw the root locus for K > 0 and find the range of K for closed-loop stability when:i. G(s) = Kii. G(s) = K(s + 200) / (s + 1000)
A closed loop unity feedback system has the forward transfer function G(s) = 10/[s(s+1) (s+2)+2]. Find the closed-loop transfer function H(s) = C(s)/R(s). Select one: a. H(s) = 10 / (s*s*s+4s*s+3s+13) b. H(s) = 10 / (s*s*s+3s*s+2s+12) c. None of the above d. H(s) = 10 / (s*s*s+5s*s+4s+14) e. H(s) = 10 / (s*s*s+2s*s+s+11)
100 y(t)+ y (t) = X(t) for a system defined by a first-order differential equation:a. Draw the log magnitude(dB)-log frequency graph of H (jw) (phase graph is not requested. it is expected that the frequency axis will also be logarithmic when plotting the log magnitude graph).b. If the magnitude of H(jw) is -40 dB, it is assumed that the input is suppressed. it is given that the signal X (t) = coswat is suppressed by this system. What is the smallest wa value in this case?
a system whose closed-loop transfer function is given by G(s)=K/s(s^2+s+1)(s+2)+K derive a Routh-Hurwitz array to determine the stability of the system.
1)The circuit shown below is initially, for t < 0, with capacitor C connected to a battery (Vbat = 12 V). The key is switched at t = 0, disconnecting the battery and turning on the capacitor to the rest of the circuit.a) Determine the energy stored in the circuit at t = 0 . b) Draw an equivalent circuit for the frequency domain, valid for t ≥ 0. Indicate the values of all components of the equivalent circuit.c) Determine the expression for the loop current in the frequency domain, I(s), expanded into partial fractions.
From a compliance transfer function of a spring-mass–damper system, the stiffness is determined to have a value of 0.6 N/m, a natural frequency of 0.50 rad/s, and a damping coefficient of 0.089 kg/s.1. Neatly derive the expressions of the magnitude and phase of the mobility transfer function

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