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1. Evaluate stability of the following systems: a) A continuous time system described by the following...
Convert the following continuous time transfer function to discrete time transfer functions with sampling rates of 0.01 and 0.1. Write with an equation editor the two discrete transfer functions. Next...
Convert the following continuous time transfer function to discrete time transfer functions with sampling rates of 0.01 and 0.1. Write with an equation editor the two discrete transfer functions. Next apply a unity feedback to the continuous transfer function and the two discrete transfer functions. Based on the poles of the closed-loop continuous transfer function, is the system stable? Why? Plot the poles of the discrete transfer functions on the z-plane. Are the two systems stable and why?
Problem 11: Discretization of a Continuous-Time Filter Consider the continuous-time system with transfer function Hc(s) A...
Problem 11: Discretization of a Continuous-Time Filter Consider the continuous-time system with transfer function Hc(s) A discrete-time approximation to the system using the [16, -8 two's complement representation scheme is to be designed (A) Using Tustin's approximation, determine a discrete-time approximation with transfer function (B) Determine the poles and zeroes of Hd,Tustin(z), noting that the poles are complex conjugates (C) Plot the frequency responses of Hd,Tustin (2) and of Hd.eract (z) Hd, Tustin (z) using the sampling time 1 ms....
1. Consider the block diagram continuous-time, linear, time-invariant system shown be- low. A Ali (a) Find...
1. Consider the block diagram continuous-time, linear, time-invariant system shown be- low. A Ali (a) Find the transfer function of the system. Show your work. (5 points) (b) Draw the canonical direct form realization of this system using multipliers, in- tegrators and adders. Show your work. If you do not know how to do part (a), you can state so, and draw the canonical realization of the system with transfer function 3s - 11 52 + 7s +12 Note: This...
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the...
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the poles and zeros b) indicate the poles and the zeros on the s-plane indicate the region of convergence (ROC) c) write the differential equation of the system. d) determine the gain of the system at dc (ie the transfer function at w=0) e) is the system described by H(s) stable? explain f) for the system described by H(s), does the Fourier transform H(jw) exist?...
For a causal LTI discrete-time system described by the difference equation:
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
Using MATLAB 4) Consider the stable second-order continuous transfer function (in s domain): H = S...
Using MATLAB
4) Consider the stable second-order continuous transfer function (in s domain): H = S +1 S2 + 3s + 2 Using the command Hd = c2d (H, Ts) with Ts = 0.1, convert H to the z domain. On the same Figure, plot the continuous impulse response of the system against the discrete one. Considering your work in problem 4, 5) Vary Ts (Ts = 0.7, 0.5, 0.3, 0.1) and observe the plot of the continuous impulse response...
The open loop transfer function of a discrete-time system is given by k (z+0.9) G (2)...
The open loop transfer function of a discrete-time system is given by k (z+0.9) G (2) = (z-1)(z-0.7) i) Draw the root locus for the system for variations in the value of K ii) Determine the marginal value of K for stability.
Question#1 Given the following block diagram of a continuous-time system with Ki 10 and K2=5 Rs)...
Question#1 Given the following block diagram of a continuous-time system with Ki 10 and K2=5 Rs) Yo) a) Using the forward rectangular rule equivalent discrete-time system (FRR), find the state- variable model (SVM) of the above system in matrix form. b) If the overall z-trans fer function of Y(z/R(2) is found to be 10z2 Y(z) R(2) 6622-57z+1 What discrete-time equivalent is used to reach to the above transfer function? Show work c) Using Y(z)/R(z) of part (b), if r(k)-a unit-step...
For each of the following discrete systems described by either its transfer function or its unit...
For each of the following discrete systems described by either its transfer function or its unit impulse response, determine if the system is asymptotically stable, marginally stable, or unstable 1. z +1 / I. 1.5% 1 0.5 (b) Mn]:e-n sin(m)11[n]
1. Use the Routh-Hurwitz test to determine if the system described by the following transfer function...
1. Use the Routh-Hurwitz test to determine if the system described by the following transfer function is stable. If the system is unstable, how many poles are outside the LHP? Use Matlab to check your answers. C() 10-8) R(s) s2 +7s +28 2. Repeat problem 1) above for the system with transfer function C (s) R(5s +Bs+ 40 s2 +2s+4 3. Use the Routh-Hurwitz test to determine if the system described by the following characteristic equation is stable. If the...
Problem 11: Discretization of a Continuous-Time Filter Consider the continuous-time system with transfer function Hc(s) A discrete-time approximation to the system using the [16, -8 two's complement representation scheme is to be designed (A) Using Tustin's approximation, determine a discrete-time approximation with transfer function (B) Determine the poles and zeroes of Hd,Tustin(z), noting that the poles are complex conjugates (C) Plot the frequency responses of Hd,Tustin (2) and of Hd.eract (z) Hd, Tustin (z) using the sampling time 1 ms....
1. Consider the block diagram continuous-time, linear, time-invariant system shown be- low. A Ali (a) Find the transfer function of the system. Show your work. (5 points) (b) Draw the canonical direct form realization of this system using multipliers, in- tegrators and adders. Show your work. If you do not know how to do part (a), you can state so, and draw the canonical realization of the system with transfer function 3s - 11 52 + 7s +12 Note: This...
Using MATLAB
4) Consider the stable second-order continuous transfer function (in s domain): H = S +1 S2 + 3s + 2 Using the command Hd = c2d (H, Ts) with Ts = 0.1, convert H to the z domain. On the same Figure, plot the continuous impulse response of the system against the discrete one. Considering your work in problem 4, 5) Vary Ts (Ts = 0.7, 0.5, 0.3, 0.1) and observe the plot of the continuous impulse response...
The open loop transfer function of a discrete-time system is given by k (z+0.9) G (2) = (z-1)(z-0.7) i) Draw the root locus for the system for variations in the value of K ii) Determine the marginal value of K for stability.
Question#1 Given the following block diagram of a continuous-time system with Ki 10 and K2=5 Rs) Yo) a) Using the forward rectangular rule equivalent discrete-time system (FRR), find the state- variable model (SVM) of the above system in matrix form. b) If the overall z-trans fer function of Y(z/R(2) is found to be 10z2 Y(z) R(2) 6622-57z+1 What discrete-time equivalent is used to reach to the above transfer function? Show work c) Using Y(z)/R(z) of part (b), if r(k)-a unit-step...
For each of the following discrete systems described by either its transfer function or its unit impulse response, determine if the system is asymptotically stable, marginally stable, or unstable 1. z +1 / I. 1.5% 1 0.5 (b) Mn]:e-n sin(m)11[n]
1. Use the Routh-Hurwitz test to determine if the system described by the following transfer function is stable. If the system is unstable, how many poles are outside the LHP? Use Matlab to check your answers. C() 10-8) R(s) s2 +7s +28 2. Repeat problem 1) above for the system with transfer function C (s) R(5s +Bs+ 40 s2 +2s+4 3. Use the Routh-Hurwitz test to determine if the system described by the following characteristic equation is stable. If the...
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