Determine a set of state equations and an output equation for the system that is described...
Determine a set of state equations and an output equation for
the system that is described by the following differential
equation. Put
the results in matrix form
y''(t)+7Y'(t)+3y(t)=4u'(t)+5u(t)
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Determine a set of state equations and an output equation for
the system that is described...
a-represent system in state space form? b-find output response y(t? c-design a state feedback gain controller? 3- A dyn...
a-represent system in state space form?
b-find output response y(t?
c-design a state feedback gain controller?
3- A dynamic system is described by the following set of coupled linear ordinary differential equations: x1 + 2x1-4x2-5u x1-x2 + 4x1 + x2 = 5u EDQMS 2/3 Page 1 of 2 a. Represent the system in state-space form. b. For u(t) =1 and initial condition state vector x(0) = LII find the outp (10 marks) response y(t). c. Design a state feedback gain...
Question 5 Following differential equations defines input-output relationships of a system with y as output and...
Question 5 Following differential equations defines input-output relationships of a system with y as output and r as inputs. d’yı + dy 2 + y, + 5 y, = 10 r, dt ? dt. dy 2 + 1 + 7y, = 8r2 dt dt at a) Define suitable state variables and find the state equation and output equation. [8marks] b) Find system matrix (A), input matrix (B) and output matrix (C). [5marks] c) Draw the state space diagram and find...
. A linear, time invariant system is described as the following state equation and output equation,...
. A linear, time invariant system is described as the following state equation and output equation, dx1/dt= -x1(t)+x2(t)+u(t) dx2/dt=-x1(t)-x2(t)+x3(t) dx3/dt=-2x2(t)+x3(t)-2u(t) y(t)=x1(t)+2x2(t)+2x3(t) re-write the state space equation as following, determine matrices A, B, C and D:dx/dt=Ax+Bu y(t)=Cx+Du(t)
2. The equations of motion of this system are; ma Seats 12Y"+7Y'+247-6Z'-122=0 6Z" + 6Z'+12Z- 6Y-12Y=f(t)...
2. The equations of motion of this system are; ma Seats 12Y"+7Y'+247-6Z'-122=0 6Z" + 6Z'+12Z- 6Y-12Y=f(t) 7W"+7W'+14W-7Y'-14Y=ft) Body Suspension Where Y,Z and W are deformations of the masses and springs. m2 Wheel Put these equations into state variable form and express the model as matrix vector equation if output of the system is Y. Road Datum level Energy Storage Element mi m2 т3 ki k2 k₃ State Variable X1 = Y' X2 = Z' X3 = W' X4 = Y...
2. The equations of motion of this system are; 12Y"+7Y'+247-62-122=0 62"' +62 +12Z- 6Y-12Y=f(t) 7W"+7W'+14W-7Y-14Y=ft) Where...
2. The equations of motion of this system are; 12Y"+7Y'+247-62-122=0 62"' +62 +12Z- 6Y-12Y=f(t) 7W"+7W'+14W-7Y-14Y=ft) Where Y,Z and W are deformations of the masses and springs. Put these equations into state variable form and express the model as matrix vector equation if output of the system is Y. Energy Storage Element State Variable mi X = Y' m2 X2 = Z' m3 X3 =W' ki X4 = Y k2 Xς k3 X6 = W Faz Seats Body Suspension Wheel Road...
The equations of motion of this system are: 12Y"+7Y'+244-6Z'-122=0 6Z" + 6Z'+12Z- 6Y’-12Y=f(t) 7W"+7W'+14W-7Y’-14Y=ft) Where Y,...
The equations of motion of this system are: 12Y"+7Y'+244-6Z'-122=0 6Z" + 6Z'+12Z- 6Y’-12Y=f(t) 7W"+7W'+14W-7Y’-14Y=ft) Where Y, Z and W are deformations of the masses and springs. Put these equations into state variable form and express the model as matrix vector equation i output of the system is Y. Seats mi Body Suspension Wheel Road Datum level Energy Storage Element mi m2 m3 ki k₂ State Variable X = Y' X2 = Z' X3 = W' X4 = Y X; =...
A dynamic system is described by a set of ordinary numbers (20 marks total) Question 3...
A dynamic system is described by a set of ordinary numbers
(20 marks total) Question 3 A dynamic system is described by a set of ordinary differential equations: 0.5x=0.05x +0.1y y 0.1x Answer the following 4 questions about this system (please use answer book for working but provide the final answers in the workbook): (a) The above system can be rewritten in matrix form as x Ax where x is the vector with solutions: x(t) y(t) X Write down the...
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or...
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
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...
a-represent system in state space form?
b-find output response y(t?
c-design a state feedback gain controller?
3- A dynamic system is described by the following set of coupled linear ordinary differential equations: x1 + 2x1-4x2-5u x1-x2 + 4x1 + x2 = 5u EDQMS 2/3 Page 1 of 2 a. Represent the system in state-space form. b. For u(t) =1 and initial condition state vector x(0) = LII find the outp (10 marks) response y(t). c. Design a state feedback gain...
Question 5 Following differential equations defines input-output relationships of a system with y as output and r as inputs. d’yı + dy 2 + y, + 5 y, = 10 r, dt ? dt. dy 2 + 1 + 7y, = 8r2 dt dt at a) Define suitable state variables and find the state equation and output equation. [8marks] b) Find system matrix (A), input matrix (B) and output matrix (C). [5marks] c) Draw the state space diagram and find...
2. The equations of motion of this system are; ma Seats 12Y"+7Y'+247-6Z'-122=0 6Z" + 6Z'+12Z- 6Y-12Y=f(t) 7W"+7W'+14W-7Y'-14Y=ft) Body Suspension Where Y,Z and W are deformations of the masses and springs. m2 Wheel Put these equations into state variable form and express the model as matrix vector equation if output of the system is Y. Road Datum level Energy Storage Element mi m2 т3 ki k2 k₃ State Variable X1 = Y' X2 = Z' X3 = W' X4 = Y...
2. The equations of motion of this system are; 12Y"+7Y'+247-62-122=0 62"' +62 +12Z- 6Y-12Y=f(t) 7W"+7W'+14W-7Y-14Y=ft) Where Y,Z and W are deformations of the masses and springs. Put these equations into state variable form and express the model as matrix vector equation if output of the system is Y. Energy Storage Element State Variable mi X = Y' m2 X2 = Z' m3 X3 =W' ki X4 = Y k2 Xς k3 X6 = W Faz Seats Body Suspension Wheel Road...
The equations of motion of this system are: 12Y"+7Y'+244-6Z'-122=0 6Z" + 6Z'+12Z- 6Y’-12Y=f(t) 7W"+7W'+14W-7Y’-14Y=ft) Where Y, Z and W are deformations of the masses and springs. Put these equations into state variable form and express the model as matrix vector equation i output of the system is Y. Seats mi Body Suspension Wheel Road Datum level Energy Storage Element mi m2 m3 ki k₂ State Variable X = Y' X2 = Z' X3 = W' X4 = Y X; =...
A dynamic system is described by a set of ordinary numbers
(20 marks total) Question 3 A dynamic system is described by a set of ordinary differential equations: 0.5x=0.05x +0.1y y 0.1x Answer the following 4 questions about this system (please use answer book for working but provide the final answers in the workbook): (a) The above system can be rewritten in matrix form as x Ax where x is the vector with solutions: x(t) y(t) X Write down the...
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
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...
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