Write
the state equations and draw the state diagram connecting the state
equation.
Draw the state diagrams for the following systems. dx(t) = Ax(t)+Bu(t) dt (a) A = -1...
Standard state-space representations of LTI systems x(t)-Ax(t)+Bu(t); yt)-Cx(t)+Du(f) Two different systems have the following representations: 0 2 -3 a. Determine the input-output transfer functions for the two systems above. Are they the same? b. Explain the result obtained in part a. c. Determine the poles and zeros of the two systems above
1. A state space linear system is shown below. dx1(t)/dt=x1(t)+x2(t)-x3(t)+u1(t) dx2(t)/dt=--x3(t)-u1(t) dx3(t)/dt=-x3(t)-u2(t) y(t)=-x1(t)+x3(t) (1) Re-write the state space equation as following, determine matrices A, B, C and D dx(t)/at=Ax+Bu y(t)=Cx+Du (2) Determine the matrix Q that is Q=[B A*B (A^2)*B (A^3)*B L (A^(n-1)*B] (3) Determine if the rank of Q is n (n=3) and determine if the system is controllable
consider the system
X(t) = ax(1) + bu(t) with a = 0.001,b= 1,x(0) = 5. (a) Simulate this system using the Matlab command initial (b) Now use u(t) = -kx(t) where k is found as the optimal gain by minimizing the performance index J= ax (1) + ru (1) dt Use q=1, r=1 to simulate this system.
please solve 8-14
8-13. Given the dynamic equations ast) = Ax(t)+ Bu(t) y(t)=Cx(t) I 0 2 0 1 To A = 120 B= 1 C= (a) 1 -1 0 1 [ 0 2 0 1 1 A = 120 B c=1017 (b) (-1 11] -2 1 0 1 A- 7 -2 0 B- C-[1 0 0] A=0 (d) [ 00 -1 832 -} - ic-[1 0] (e) -2 -3 8-14. For the systems described in Prob. 8-13, find the transformation...
1. If A= [ 1 = [] 4]. find the general solution to dx dt Ax
Solve the following systems of DE in the form dX -= A_, X(t) where A are given as follows: (40 pts) dt c) [-10 0 A- 1 5 - 1 6 -2 (10 pts) (10 pts)
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
(a) Consider the system i = Ax + bu where 1-1::) and b = (b1 b2). Derive a necessary and sufficient condition on the matrix b (i.e., bi and b2) for complete controllability of the system. (b) Same as part (a), except that 0 -1 A= 1 0
5. [-/2 Points] DETAILS SCALCLS1 10.2.025. Solve the initial value problem dx/dt = Ax with x(0) = Xo. A-[3] [2] x(t)
dx Determine x= f(t) for (t? +4t) 4x + 4,t> 0; f(1) = 3. dt For (1? + 4t) dx dt = 4x +4, x= f(t) =