Find the transfer functions of the processes described by the following models (y is output, u, u1,u2,u3 are input variables):
a.) dy/dt = u1^2 + e^2u2 + u1u3
b.) dy/dt = u1cos u2
Find the transfer functions of the processes described by the following models (y is output, u,...
Find the transfer functions of the processes described by the following models (y is output, u, u1,u2,u3 are input variables): dy/dt=u1*cos(u2)
Find the transfer function from the input u to the output y, for each of the following systems: (a) y + 3y + 5y = 8u (b) y= 3.1 + 2r, + 9.2 + 4.r = u 2ų – 12y - y = 7u – 3u dy dy = 3u - 1 d76-34 d3 + 2.sodu d44-u, d73 +84 dt Y(S) Hint: The Laplace operator is linear, and thus ; X(s) Y(s) U(s) U(s) X(5)
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...
1.2 [12 points] Determine the transfer functions for the following systems. (a) A system described by the signal flow graph below: -1 Figure 2 (b) A second-order system with input u and output y described by the state variable model below: i- Ax + Bu y -2x, 01 where x- A-TT
An LTI system is described by the following differential equation. Find the output when x(t)- u(t) and has the following initial conditions: y(0)= 1, (0) = 2 , and x(0)--I dy x dx +at + 4 y(t) = dt + x(t) Solution
a system is given by the following transfer function Y(s)/u(s) = 1/(s^2-16) a)find the output in time domain Y(t) if the input u(t) is a unit step. (Hint the transfer function of the unit step function is 1/s) b)what is Y(t) as t goes to infinity
11. Using generating functions, find the number of solutions of the equation 6, u1 +u2+... +u -22, where 1 < 6, i-1,...,4, 2 Suj ui (For (.) type C(6,4).) 11. Using generating functions, find the number of solutions of the equation 6, u1 +u2+... +u -22, where 1
11. Using generating functions, find the number of solutions of the equation 6, u1 +u2+... +u -19, where 1 < 7,i,...,4, 2 Suj ui 9. (For () type C(6,4).) 11. Using generating functions, find the number of solutions of the equation 6, u1 +u2+... +u -19, where 1
For each of these utility functions, b. Compute the MRS. c. Do these tastes have diminishing marginal rates of substitution? Are they convex? d. Construct an indifference curve for each of these functions for utility numbers U1 = 10 , U2 = 100 , U3 = 200 . e. Do these utility functions represent different preference orderings? 1. Consider the following utility functions: (i) U(x,y)- 6xy, (ii) U(x,y)=(1/5)xy, MU,--y and MU,--x ii) U(x,y)-(2xy)M 8xy2 and MUy -8x2y MU,-6y and...
3. Consider the causal single input single output system described by the transfer function (6s + 1)(4s + 3) 53 + 8s² + 19s +2 Y(s) U(s) Using the phase variable decomposition method express in terms of the state vector x, state matrix A, input matrix B and output matrix C.