Problem 4. Obtain state-space equations of a system described by the following differential equations: mi b
A Mechanical system is shown in Fig. 1.1. a) Obtain a set of simultaneous integro-differential equations, in terms of velocity, to represent the system, where k is spring Constant, m is the mass and b is damper. (Hint: draw two Free Body Diagrams and obtain two equations in terms of x1 and x2 only). X1 - Ft mi m2 M TTTTTTTTYYTTTTTTTTTYYTTTTTTT Fig 1.1 b) What components and energy source do you need to use in order to build an electric...
a-obtain state space representation b-obtain system eigen values c-diagnolize the system Question (3: (10 Marks) For the following system, U(s) s + 5 (s +2) (s +3) s + 1 Obtain a state space representation in the controllable canonical form. (4 marks) b) Obtain the system eigen values, (3 marks) c) Diagonalize the system. (3 marks) a) Page 2 DQMS 2/3 Question (3: (10 Marks) For the following system, U(s) s + 5 (s +2) (s +3) s + 1...
Problem 1 (25 points): Consider a system described by the differential equation: +0)-at)y(t) = 3ú(1); where y) is the system output, u) is the system input, and a(t)is a function of time t. o) (10 points): Is the system linear? Why? P(15 points): Ifa(t) 2, find the state space equations?
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)
am Problem 3 Given the system of linear differential equations and initial condi- tions Initial conditions x(0), y(0)0 a. Use Cramer's rule (i.e. Matrix method) to obtain differential equations for x and y. am Problem 3 Given the system of linear differential equations and initial condi- tions Initial conditions x(0), y(0)0 a. Use Cramer's rule (i.e. Matrix method) to obtain differential equations for x and y.
9. For the transfer function: Find its state space representation. 10. A system is described by the following differential equations: Find its state space representation.
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...
Consider the following linear system of differential equations: dx/dt = 2x-3y dy/dt = -x +4y (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given x(0) = 3 and y(0) = 4 (d) Verify the calculations with MATLAB
1. For the mechanical system shown, A. Obtain the differential equations and set them in the matrix form. 2m B. find the natural frequencies and related amplitude ratios as functions of m and k. C. For m 4 Kg, k= 100 N/m, x,(0) 1, X2(0) 1, 1 (0) 0, *2(0) 0, find x (t) and x2 (t) in normal and general vibrations E WW 1. For the mechanical system shown, A. Obtain the differential equations and set them in the...
Obtain a state-space representation of the system shown below yI 7m Obtain a state-space representation of the system shown below yI 7m