5. SVM: Drive the SVM models: *=Ax+Br , Output: y=Cx+Dr for the system below (D=d/dt): Assume...
tablish the state equations describing the system below R(s) c) Define the state variables in a block diagram d) Define A, B and Cin the state equations: (t)-Ax(t)+ Br() yt) Cx(t) tablish the state equations describing the system below R(s) c) Define the state variables in a block diagram d) Define A, B and Cin the state equations: (t)-Ax(t)+ Br() yt) Cx(t)
6. Consider a state-space system x = Ax+ Bu, y = Cx for which the control input is defined as u- -Kx + r, with r(t) a reference input. This results in a closed-loop system x (A-BK)x(t)+ Br(t) = with matrices 2 -2 K=[k1 K2 For this type of controller, ki, k2 ER do not need to be restricted to positive numbers - any real number is fine (a) What is the characteristic equation of the closed-loop system, in terms...
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine the type of the equilibrium point at the origin. (35 points) (b) Find all straight-line solutions and draw the phase portrait for the system. (35 points) (c) What is the general solution to the system? (15 points) (d) Find the solution of the system with initial conditions: x(0) = 1 and y(0) = -1. (15 points)
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
Solve the following equations for the variables specified. (a) x=43(y−3)+y, for y. (b) ax+b=cx−d, for x. (c) 2KL1/3=Y0, for L. (d) qx−py=m, for y. (e) (1/r−a) / (1/r+b) =c, for r. (f) Y= a(Y−tY−k)+b+I+G0+cY, for Y. SHOW YOUR WORK
q We would like to fit a line y = cx + d to the following data х у -1 -3 0 -1 0 2 3 using the method of least squares. (a) Write down the (overdetermined) linear system this problem gives rise to in the form Ax = b, where x = (..) (b) Find the best-fit line by computing the least-squares solution of the system Ax = b.
3) Consider the system depicted below xz Input: F. Output: x Assume that all initial conditions are zero. a) Derive mathematical model of the system b Find unit step response c) Find the transfer function T(s) X2(s)/Fs) d) What is the final value of the output be. limx)-7) for F)- 4) Find the transfer function state space R(s) for each of the following sytems represented in a) 10 y-[1 0 0 b) 2 -3-8 3 -5 y-1 3 6 c)...
use taylor expansion please to linearize 3 Given the equations of state: dxi/dt -sec(xi +r2) 2, dx2/dt -u + y here y is the output of a system and we consider a XI +π/4, state-space vector, x: Identify locations of stability for this system, where dx/dt = 0. Since we are dealing with trigonometric functions there will be multiple stability points, but notice that your choice should not affect the following sections of this problem Linearize to determine A such...
3 Given the equations of state: dxi/dt -sec(xi +r2) 2, dx2/dt -u + y here y is the output of a system and we consider a XI +π/4, state-space vector, x: Identify locations of stability for this system, where dx/dt = 0. Since we are dealing with trigonometric functions there will be multiple stability points, but notice that your choice should not affect the following sections of this problem Linearize to determine A such that x = Ax A B...
slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute the transfer function Y(s)/U(s)? B)Find inverse Laplace for y(t) and x(t)? C) find the final value of the system? D)find the initial value of the system? Please solve clearly with steps.