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June 18, 2019 2. A system is characterized by the following differential equation: (18 pts) y)...
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...
For the given RC circuit shown below, ys the output, and ut) is the input. Values of the components are marked on schematic i) Derive the system differential equation and transfer function Y(s)/U(s)...
For the given RC circuit shown below, ys the output, and ut) is the input. Values of the components are marked on schematic i) Derive the system differential equation and transfer function Y(s)/U(s) ii) Choose voltage across capacitors as states and derive the state equations and state matrices (A, B, C,and D). iii) Validate the states by deriving the transfer function from state matrices. iv) Choose a different set of states and derive a different state equation and state Matrix...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y +...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
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...
Given the System described by the differential equation below: D^2 y(t) + 3 Dy(t) + 2y(t)...
Given the System described by the differential equation below: D^2 y(t) + 3 Dy(t) + 2y(t) = x(t) where D=d/dt and D^2 is the second derivative 1) find its Transfer Function H(s) (assume all initial conditions are zero) 2) use the first procedural way of getting A, B, C, D from H(s) to find the corresponding state space representations . Then do the reverse step of finding H(s) from the A, B, C, D representation just found (i.e. check that...
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...
SKEE 313 SKEU 3133 Q.3 (a) A linear dynamic system is characterized by the following equations,...
SKEE 313 SKEU 3133 Q.3 (a) A linear dynamic system is characterized by the following equations, xi(t) + 2x2(t) = 3x1(t) + 4x2(t) – 5u(t) xi(t) – x2(t) = 2xı(t) + x2(t) + u(t) y(t) = xi(t) + 2x2(t) where: u(t): input y(t): output xi(t) dan xz(t): state variables Write the system's state space representation, (the state and output equations) in matrix format. (6 marks)
2 A robot-arm drive system for one joint can be represented by the differential equation dv...
2 A robot-arm drive system for one joint can be represented by the differential equation dv kvt)k2y(t)+ kyi(t) dt position, and i(t) is the control-motor current velocity, y(t) Where v(t) Derive the state-space equation of the system a) (5 marks) b) By using Routh-Hurwitz criterion, determine the conditions for k,k2,and ky so that the system remains stable? (5 marks)
2 A robot-arm drive system for one joint can be represented by the differential equation dv kvt)k2y(t)+ kyi(t) dt position, and...
Exact Solution of 1st-order system of Differential Equations Find the Particular solution of the following differential...
Exact Solution of 1st-order system of Differential Equations
Find the Particular solution of the following differential
equation with the initial conditions:
pls don't solve this using matrices.
ー-3-2y, x(t = 0) = 3; 5x - 4y
Question: given a differential equation: a. initial conditions for the plan and input are zero, ...
Question:
given a differential equation:
a. initial conditions for the plan and input are zero, derive
plan's transfer function in Laplace transform
b. using inverse Laplace transform, find the solution for the
differential equation for the plan (find function y(t)).
c. derive state-space model of the plan
d. Assume open-loop system with no controller added to the
plant, analyse the steady-state value of the system using final
value theorem and step input
e. Calculate value of the overshoot, rise time...
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...
For the given RC circuit shown below, ys the output, and ut) is the input. Values of the components are marked on schematic i) Derive the system differential equation and transfer function Y(s)/U(s) ii) Choose voltage across capacitors as states and derive the state equations and state matrices (A, B, C,and D). iii) Validate the states by deriving the transfer function from state matrices. iv) Choose a different set of states and derive a different state equation and state Matrix...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
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...
SKEE 313 SKEU 3133 Q.3 (a) A linear dynamic system is characterized by the following equations, xi(t) + 2x2(t) = 3x1(t) + 4x2(t) – 5u(t) xi(t) – x2(t) = 2xı(t) + x2(t) + u(t) y(t) = xi(t) + 2x2(t) where: u(t): input y(t): output xi(t) dan xz(t): state variables Write the system's state space representation, (the state and output equations) in matrix format. (6 marks)
2 A robot-arm drive system for one joint can be represented by the differential equation dv kvt)k2y(t)+ kyi(t) dt position, and i(t) is the control-motor current velocity, y(t) Where v(t) Derive the state-space equation of the system a) (5 marks) b) By using Routh-Hurwitz criterion, determine the conditions for k,k2,and ky so that the system remains stable? (5 marks)
2 A robot-arm drive system for one joint can be represented by the differential equation dv kvt)k2y(t)+ kyi(t) dt position, and...
Exact Solution of 1st-order system of Differential Equations
Find the Particular solution of the following differential
equation with the initial conditions:
pls don't solve this using matrices.
ー-3-2y, x(t = 0) = 3; 5x - 4y
Question:
given a differential equation:
a. initial conditions for the plan and input are zero, derive
plan's transfer function in Laplace transform
b. using inverse Laplace transform, find the solution for the
differential equation for the plan (find function y(t)).
c. derive state-space model of the plan
d. Assume open-loop system with no controller added to the
plant, analyse the steady-state value of the system using final
value theorem and step input
e. Calculate value of the overshoot, rise time...
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