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5. A two-input, two-output dynamic system is defined by the following differential equations syst...
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)
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...
the following problem is of a two-mass system. I have 2 questions 1. find the transfer...
the following problem is of a two-mass system. I have 2
questions
1. find the transfer function from input F2 to output x1
2. for the transfer function found, determine the sensitivity to
variation in parameter B12
note: i already found the differential eqns of motion for
t>0
Problem formulation Two masses are connected as shown in Fig. 1. Input forces Fi(t) and F.(t) act on masses m, and mg, respectively. The outputs are positions xi(t) and x2(t). Initial conditions...
5. A dynamic system is modeled as (ult) u2t) to the output (vi(t) (u) un 0 80 Calculate the trans...
please help
5. A dynamic system is modeled as (ult) u2t) to the output (vi(t) (u) un 0 80 Calculate the transfer function matrix connecting the input (uit y2(t), all initial conditions equal to O
5. A dynamic system is modeled as (ult) u2t) to the output (vi(t) (u) un 0 80 Calculate the transfer function matrix connecting the input (uit y2(t), all initial conditions equal to O
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).
10. Solve the system of differential equations by using eigenvalues and eigenvectors. x1 = 3x, +...
10. Solve the system of differential equations by using eigenvalues and eigenvectors. x1 = 3x, + 2x2 + 2xz x2 = x + 4x2 + x3 X;' =-2x, - 4x2 – x3
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).
solve all 22. The input-output relationship for a linear, time-invariant system is described by differential equation...
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
dv11 ch • Exercise • For the system defined by the following differential equations, find the...
dv11 ch • Exercise • For the system defined by the following differential equations, find the system transfer function H(s)=V(s)/(s) 1). ) drdt dv d v).. chut +6v *6.91 d di? - +57(0) dr de
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state d...
State space of transfer function
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state diagram of the system. Obtain the dynamic equations of the system in CCF. i.i Obtain the dynamic equations of the system in odr.
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state diagram of the system. Obtain the dynamic equations of the system in CCF. i.i Obtain the dynamic equations of the...
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)
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...
the following problem is of a two-mass system. I have 2
questions
1. find the transfer function from input F2 to output x1
2. for the transfer function found, determine the sensitivity to
variation in parameter B12
note: i already found the differential eqns of motion for
t>0
Problem formulation Two masses are connected as shown in Fig. 1. Input forces Fi(t) and F.(t) act on masses m, and mg, respectively. The outputs are positions xi(t) and x2(t). Initial conditions...
please help
5. A dynamic system is modeled as (ult) u2t) to the output (vi(t) (u) un 0 80 Calculate the transfer function matrix connecting the input (uit y2(t), all initial conditions equal to O
5. A dynamic system is modeled as (ult) u2t) to the output (vi(t) (u) un 0 80 Calculate the transfer function matrix connecting the input (uit y2(t), all initial conditions equal to O
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).
10. Solve the system of differential equations by using eigenvalues and eigenvectors. x1 = 3x, + 2x2 + 2xz x2 = x + 4x2 + x3 X;' =-2x, - 4x2 – x3
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).
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
dv11 ch • Exercise • For the system defined by the following differential equations, find the system transfer function H(s)=V(s)/(s) 1). ) drdt dv d v).. chut +6v *6.91 d di? - +57(0) dr de
State space of transfer function
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state diagram of the system. Obtain the dynamic equations of the system in CCF. i.i Obtain the dynamic equations of the system in odr.
10. Consider the following input-output transfer function. U(s) s3 6s 11s +4 Draw the CCF state diagram of the system. Obtain the dynamic equations of the system in CCF. i.i Obtain the dynamic equations of the...
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