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Answer all questions ELE380: Control Systems I Homework #1 Due: 10/3/2018 1. The circuit of a bridged-T network is shown below. R2 CIC Show that the transfer function of the network is Vo (s)12R,Cs +R,R2C2s Vin(s) 1 (2R1 R2)Cs R,R2C2s2 Sketch the pole-zero diagram when R 0.5, R2 1,C 0.5 (Hint: One way is to start by writing KCL equations in the s-domain for nodes I and 2) 2. A feedback control system has the structure shown below. Determine the...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from Definition)- For (c) r(t) = te-2, 11(1) (b) x(t)-2t rect(t) 1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from...
Closed-loop system response and characteristics, Proportional gain 10 < paste transfer function Ts as output from Matlab here> clear all: close all: ls J = 0.022R = 0.11;K = 0.02;R 1.5;L= 0.6; Closed loop Transfer function T(s) Cs-10; RRA pole (Tg) 22T zero (Tg) figure ; figure ; teS) characteristics natural frequency damping ratio Dr-abs(real (RpT (2)) ) / ettling time peak time ER忌 overshoot 032=100 rise time Step response of open-loop system: Pole-zero map: easte,pole-zero plot here> Pole-Zero Map...
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() = K(+2) s(s+ 1/s + 3)(+5) a) Sketch the root locus. Clearly indicate any asymptotes. b) Find the value of the gain K, that will make the system marginally stable. c) Find the value of the gain K, for which the closed-loop transfer function will have a pole on the real axis at (-0.5).
1. Given a baseband signal m(t) sin(1000mt) cos(3000nt) + cos(3700nt a. Sketch the spectrum of m(t) (Hint. sin(a) cos(b) 0.5 sin(a +b) +0.5sin a-b)) b. Sketch the spectrum of DSB-CS signal m(t)cos(10000mt) C ldentify the upper sideband {USB) and lower sideband (LSB) spectra d. Give the black diagram of the receiver to receive DSB-CS signal in (b). 2. baseband signal m(r)--0.5 + Σ..小(t-n)-u(t-0.5-n)] where ult) is the Given unit step function, an amplitude modulated signal is as SAM 107+ m(0cos...
i)Derive (showing detailed steps) the transfer function T(s)? put T(s) in the standard format and hence show that ? ii)show that m=4Q and w=2q/rc Let R=10k Ω , compute the value of the capacitor C in order to obtain a second Butterworth (i.e. maximally flat) filter with ωp=10 rad/seconds and Amax=0.5 dB.? ion 1 (12 Mar Consider the given Single-Amplifier Biquadratic (SAB) active low-pass filter circuit (to the right) i. Derive (showing detailed steps) the transfer function T(s)Vofthis circuit, please...
Q1. Determine the solution of x(t). 4x + 20% +36x = 0 Where x(0) = 2 m, 8(0) = 1 m/s Q1. Mass M is lifted by a pulley system as shown in Figure 1. The pulley is rotating in a clockwise direction. Assuming zero initial conditions, obtain transfer function of the system, X(s)/Ta(s). Τα S B X м k Figure 1 Consider the liquid level system shown in Figure 1. At steady state, the inflow rate and outflow rate...
0.552 +0.5 102 s² + +1 S In Fig. 4.4, R=0.2 M2, C=25 pF and L=0.04 H. Show that the transfer function H(s) is: 1,(s) H(S) = I(S) 1012 10 (a) Plot the pole-zero diagram of H(s). (b) What filter is given by H(s)? Why? (c) Determine the resonant frequency 0., the quality factor Q, the cut-off frequencies 01 and 02 and the bandwidth B. i (t) w ift) R Fig. 4.4 jo
5) Consider the following second-order bandpass filter. As input voltage, apply V(t) 100Ω, C-4.7 μF. and L-10mH. sin(wt).R in Vout Fig 9: Second-order band-pass filter a) Determine the frequency response function H(ju) Ve-ju) / Vm(ju) and sketch the magnitude and phase characteristics versus w by calaulation. Calculate the theoretical cutoff frequency of the filter Using PSpice AC analysis, plot magnitude lHju)l and phase ф characteristics of the filter, between 1 Hz-100 KHz b) c) 5) Consider the following second-order bandpass...