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?
Homework Answers
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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...
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....
A unity gain negative feedback system has an open-loop transfer function given by 4. s) =...
A unity gain negative feedback system has an open-loop transfer function given by 4. s) = s(1 + 10s)(1 + 10s)? Draw a Bode diagram for this system and determine the loop gain K required for a phase margin of 20 deg. What is the gain margin? 5. We are given the closed-loop transfer function 10(s + 1) T(s) = 82+98+10 for a "unity feedback" system and asked to find the open-loop transfer function, generate a log-magnitude-phase plot for both...
you can use matlab to solve 1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The...
you can use matlab to solve
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The appropriate sampling time d) G(z) pulse transfer function e) Continuous State Space, A, B, C, D f) Discrete State Space, A, B, C, D
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of...
Give me the explanation plz 2. a) A digital controller implementation for a feedback system is shown in Figure 2 where the sampling period is T0.1 second. The plant transfer function is s +10 P(s) =...
Give me the explanation plz
2. a) A digital controller implementation for a feedback system is shown in Figure 2 where the sampling period is T0.1 second. The plant transfer function is s +10 P(s) = and the feedback controller, K, is a simple proportional gain (K>0).v R(z) E(z) S+10 Controller ZOH Plant Figure 2* i)o In order to directly design a digital controller in the z-domain, the plant P(s) 6. needs to be discretised as P(z). Find the ZOH...
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...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) fil...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
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?...
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polyno...
Please do part C only, thank you.
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polynomials, ratios of polynomials, partial fraction expansions and transfer functions: see, for example, the commands roots, poly, conv, residue, zpk and tf (a) Use MATLAB to gener ate the continuous-time transfer function H5+15)( +26(s+72) s(s +56)2(s2 +5s +30) H(s) displaying the result in two forms: as (i) the given ratio of factors and (ii) a ratio of two polynomials. (b) Use...
2:50 PM Sun May 12 89%- X 2012 Spring All Exams.pdf 5. (30 pts) A unity feedback system has the loop transfer function shown below. a) Draw the complete Nyquist HG(s)-plane plot for both small K...
2:50 PM Sun May 12 89%- X 2012 Spring All Exams.pdf 5. (30 pts) A unity feedback system has the loop transfer function shown below. a) Draw the complete Nyquist HG(s)-plane plot for both small K and large K. Use the Nyquist Path which encloses the pole of HG(s) that is at the origin. No other path will be accepted. b) Determine whether the closed loop system is stable for both small K and large Argue in terms of the...
1. A system with unity feedback is shown below. The feed-forward transfer function is G(s). Sketch...
1. A system with unity feedback is shown below. The feed-forward transfer function is G(s). Sketch the root locus for the variations in the values of pi. R(9)+ 66) 69? Fig. 1: Unity-feedback closed-loop system G(s)= 100 s(s+ p) 2. The following closed-loop systems in Fig. 2 and Fig. 3 are operating with a damping ratio of 0.866 (S =0.866). The system in Fig. 2 doesn't have a PI controller, while the one in Fig. 3 does. Gain Plant R(S)...
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....
A unity gain negative feedback system has an open-loop transfer function given by 4. s) = s(1 + 10s)(1 + 10s)? Draw a Bode diagram for this system and determine the loop gain K required for a phase margin of 20 deg. What is the gain margin? 5. We are given the closed-loop transfer function 10(s + 1) T(s) = 82+98+10 for a "unity feedback" system and asked to find the open-loop transfer function, generate a log-magnitude-phase plot for both...
you can use matlab to solve
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The appropriate sampling time d) G(z) pulse transfer function e) Continuous State Space, A, B, C, D f) Discrete State Space, A, B, C, D
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of...
Give me the explanation plz
2. a) A digital controller implementation for a feedback system is shown in Figure 2 where the sampling period is T0.1 second. The plant transfer function is s +10 P(s) = and the feedback controller, K, is a simple proportional gain (K>0).v R(z) E(z) S+10 Controller ZOH Plant Figure 2* i)o In order to directly design a digital controller in the z-domain, the plant P(s) 6. needs to be discretised as P(z). Find the ZOH...
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...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
Please do part C only, thank you.
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polynomials, ratios of polynomials, partial fraction expansions and transfer functions: see, for example, the commands roots, poly, conv, residue, zpk and tf (a) Use MATLAB to gener ate the continuous-time transfer function H5+15)( +26(s+72) s(s +56)2(s2 +5s +30) H(s) displaying the result in two forms: as (i) the given ratio of factors and (ii) a ratio of two polynomials. (b) Use...
2:50 PM Sun May 12 89%- X 2012 Spring All Exams.pdf 5. (30 pts) A unity feedback system has the loop transfer function shown below. a) Draw the complete Nyquist HG(s)-plane plot for both small K and large K. Use the Nyquist Path which encloses the pole of HG(s) that is at the origin. No other path will be accepted. b) Determine whether the closed loop system is stable for both small K and large Argue in terms of the...
1. A system with unity feedback is shown below. The feed-forward transfer function is G(s). Sketch the root locus for the variations in the values of pi. R(9)+ 66) 69? Fig. 1: Unity-feedback closed-loop system G(s)= 100 s(s+ p) 2. The following closed-loop systems in Fig. 2 and Fig. 3 are operating with a damping ratio of 0.866 (S =0.866). The system in Fig. 2 doesn't have a PI controller, while the one in Fig. 3 does. Gain Plant R(S)...
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