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3. (25 points) For parts a & b, determine the state space representation and write the matlab cod...
3. a) Find a state space representation for a linear system represented by the following differen...
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
3. a) Find a sate space representation for a linear system represented by the following different...
3. a) Find a sate space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(0) is the output: 4y(t)- 2(t)-2y(t)3(t) b) Consider a linear system represented by the following differential equation, where st) denotes the input and yt) is the output: )+4() +4y(t)x(t) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input...
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of...
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 192 m V:(t) 1 H 1F volt) Figure 1
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of...
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) (10 MARKS] 122 112 112 M + + vi(t) 1 H llll 1 H elle 1F vo(t)
A state space linear system is shown below. Use Matlab to solve the following problems. Requirement...
A state space linear system is shown below. Use Matlab to solve the following problems. Requirement for project report: (1) Results; (2) Matlab code. dx1/dt=-x1(t)+u(t) dx2/dt=x1(t)-2x2(t)-x3(t)+3u(t) dx3/dt=-3x3(t) y(t)=-x1(t)+2x2(t)+x3(t)+u(t) (1) Assume the system has input u(t)=e-3t if t>t0 and zero initial state x(0)=[0;0;0]. Using the transition matrix obtained, compute the system’s output (analytical solution), and plot the output as a function of time (t within 0 to 10). (2) Using the function lsim to simulate the system’s output (analytical solution), and...
a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit...
a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 1 Ω 192 112 W vi(t) 1 H elle 1 H Illl 1 F volt) Figure 1
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of...
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 112 M M w + + Vilt) 1 H sooo 1 H nooo 1F vo(t) Figure 1
Matlab Homework #4: Matlab Linear Systems Simulation 1.) Obtain the differential equation for the...
Matlab Homework #4: Matlab Linear Systems Simulation 1.) Obtain the differential equation for the mechanical system shown below bi FLR) orce CN) voltege ) 2.) Obtain the differential equation for the electrical system shown below shown below OAF 3.) Find the transfer functions corresponding to the differential equations found in questions I and 2 the 4) Let the input force applied to the block of the mechanical system be zero U)-のThe initial conditions are y(0) = 10 cm and dy(0)d-0....
Problem 4: (65 points) Let a system be given by the state space representation 8 8...
Problem 4: (65 points) Let a system be given by the state space representation 8 8 10 * = X+ u(t), y = [1 -1]x – u(t) 1 1 -1 0 Y(S) d) (7) Find the transfer function US) e) (5) Is the system BIBO stable? 3 f) (9) Let the initial state x(0) -3 u(t) = 0) for all t > 0. = Find the zero input response (i.e., with the input
question 3 Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space...
question 3
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 122 w 1H lell 1H llll 1F vo(t) Figure 1
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
3. a) Find a sate space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(0) is the output: 4y(t)- 2(t)-2y(t)3(t) b) Consider a linear system represented by the following differential equation, where st) denotes the input and yt) is the output: )+4() +4y(t)x(t) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input...
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 192 m V:(t) 1 H 1F volt) Figure 1
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) (10 MARKS] 122 112 112 M + + vi(t) 1 H llll 1 H elle 1F vo(t)
a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 1 Ω 192 112 W vi(t) 1 H elle 1 H Illl 1 F volt) Figure 1
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 112 M M w + + Vilt) 1 H sooo 1 H nooo 1F vo(t) Figure 1
Matlab Homework #4: Matlab Linear Systems Simulation 1.) Obtain the differential equation for the mechanical system shown below bi FLR) orce CN) voltege ) 2.) Obtain the differential equation for the electrical system shown below shown below OAF 3.) Find the transfer functions corresponding to the differential equations found in questions I and 2 the 4) Let the input force applied to the block of the mechanical system be zero U)-のThe initial conditions are y(0) = 10 cm and dy(0)d-0....
Problem 4: (65 points) Let a system be given by the state space representation 8 8 10 * = X+ u(t), y = [1 -1]x – u(t) 1 1 -1 0 Y(S) d) (7) Find the transfer function US) e) (5) Is the system BIBO stable? 3 f) (9) Let the initial state x(0) -3 u(t) = 0) for all t > 0. = Find the zero input response (i.e., with the input
question 3
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 122 w 1H lell 1H llll 1F vo(t) Figure 1
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