Homework Answers
Simulink block diagram is given below.
case1 : initial conditions [0;0]
The response is plotted below.
case2 : initial conditions [1;0]
The response is plotted below.
case3 : initial conditions [0;1]
The response is plotted below.
case4 : initial conditions [1;1]
The response is plotted below.
State-space block where the initial conditions can be entered is given below
![Block Parameters: State-Space State Space State-space model: dx/dt Ax Bu Parameters Α, 1-20-1-1] -201-1 B: C: [o 1] Initial c](http://img.homeworklib.com/images/4f0ae914-c506-405f-8be1-ba2e65a7fab8.png?x-oss-process=image/resize,w_560)
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A system (a plant) is represented as a state-space model in the form: dt (1) Deduce and draw a si...
Consider the system simulation diagram of Figure 1. This figure shows a simulation diagram form used in the area of automatic control where x[n] is the input, y[n] is the output, and D is the unit shi...
Consider the system simulation diagram of Figure 1. This figure
shows a simulation diagram form used in the area of automatic
control where x[n] is the input, y[n] is the output, and D is the
unit shift (or delay) operator.
1. Suppose x[n] = 0.8 nµ[n] and assuming zero initial conditions
(i.e y[−1] = y[−2] = 0), write a MATLAB program that solves for
y[n], 0 ≤ n ≤ 10. Plot both the input signal x[n] and the output
signal...
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...
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measur...
control system with observer
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
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...
please help. Note: u(t) is unit-step function Consider the system with the differential equation: dyt) +...
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
a can be skipped Consider the following second-order ODE representing a spring-mass-damper system for zero initial...
a can be skipped
Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): 2x + 2x + x=u, x(0) = 0, *(0) = 0 where u is the Unit Step Function (of magnitude 1). a. Use MATLAB to obtain an analytical solution x(t) for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for x(t). Also obtain a plot of .x(t) (for a simulation of 14 seconds)...
Problem 2: Consider again the two RLC circuits from HW1 Problem 6 C L IKs IKs...
Problem 2: Consider again the two RLC circuits from HW1 Problem 6 C L IKs IKs L In HW1 Problem 6 you found the transfer function Vc(s)V(s) for each of the circuits, using Impedance Analysis. You essentially assumed zero initial conditions (for the capacitor's voltage S and for the inductor's current) 2.1. Develop a state-variable model for each of the circuits, where the state variables are (in both circuits) xi vc and x2 i That is, derive (for each circuit)...
System and computer engineering Model the dynamic systems in STAT VARIABLE form define the order of...
System and computer engineering
Model the dynamic systems in STAT VARIABLE form
define the order of the system first. Then dram simulation
diagram
Model the following dynamic systems in state variable form. Clearly define the energy storage devices and the corresponding state variables which define the energy in each device. Define the order of the system. Draw the simulation diagram for each system. 4.Input is e(t) Output is edt) e Le)
UestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Fin...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
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...
Consider the system simulation diagram of Figure 1. This figure
shows a simulation diagram form used in the area of automatic
control where x[n] is the input, y[n] is the output, and D is the
unit shift (or delay) operator.
1. Suppose x[n] = 0.8 nµ[n] and assuming zero initial conditions
(i.e y[−1] = y[−2] = 0), write a MATLAB program that solves for
y[n], 0 ≤ n ≤ 10. Plot both the input signal x[n] and the output
signal...
control system with observer
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
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...
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
a can be skipped
Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): 2x + 2x + x=u, x(0) = 0, *(0) = 0 where u is the Unit Step Function (of magnitude 1). a. Use MATLAB to obtain an analytical solution x(t) for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for x(t). Also obtain a plot of .x(t) (for a simulation of 14 seconds)...
Problem 2: Consider again the two RLC circuits from HW1 Problem 6 C L IKs IKs L In HW1 Problem 6 you found the transfer function Vc(s)V(s) for each of the circuits, using Impedance Analysis. You essentially assumed zero initial conditions (for the capacitor's voltage S and for the inductor's current) 2.1. Develop a state-variable model for each of the circuits, where the state variables are (in both circuits) xi vc and x2 i That is, derive (for each circuit)...
System and computer engineering
Model the dynamic systems in STAT VARIABLE form
define the order of the system first. Then dram simulation
diagram
Model the following dynamic systems in state variable form. Clearly define the energy storage devices and the corresponding state variables which define the energy in each device. Define the order of the system. Draw the simulation diagram for each system. 4.Input is e(t) Output is edt) e Le)
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
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...
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