Mechanic system u is an mput porce, delermine the stale space b, u reprerentahon op the syilan b2 Mechanic system u is an mput porce, delermine the stale space b, u reprerentahon op the syil...
B2. Find the steady-state errors for inputs of 5 u(t), 5t-u(t), and 5t-u(t) to the system shown in the following figure. The function u(t) is the unit step. R(S) + E(S) C($) 120(s + 2) (s + 3)(s +4)
4, (a) (20%) Find the transfer function Xi(s) / U(s) for the system shown in Fig. 2. (b) (20%) obtain a state-space model of the system shown in Fig. 2, where u is the input and x is the output. k2 kj m2 b2
Let B = {b1,b2, b3} be a basis for a vector space V. Let T be a linear transformation from V to V whose matrix relative to B is [ 1 -1 0 1 [T]B = 2 -2 -1 . 10 -1 -3 1 Find T(-3b1 – b2 - b3) in terms of bı, b2, b3 .
5 Under what condition on b,b2, bs is this system solvable? Include b as a fourth column in elimination. Find all solutions when that condition holds: 2a + 5y - 4z b2 5 Under what condition on b,b2, bs is this system solvable? Include b as a fourth column in elimination. Find all solutions when that condition holds: 2a + 5y - 4z b2
(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
2. Consider the system 2n+4x2 + 8x3 + 12n = b2 (a) Reduce A b to Row Reduced Echelon Form Rx-c (b) Find the condition on bi, b2, bs for Ax b to have a solution (c) Find the nullspace of A as the span of special solutions (d) Find a particular solution when b- 3 6 9 and the general solution.
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...
Assume that the transition matrix from basis B = {b1, b2, b3} to basis C = {c1, c2, c3} is PC,B = 1/2*[ 0 -1 1 ; -1 1 1 ; 1 0 0 ]. (a) If u = b1 + b2 + 2b3, find [u]C. (b) Calculate PB,C. (c) Suppose that c1 = (1, 2, 3), c2 = (1, 2, 0), c3 = (1, 0, 0) and let S be the standard basis for R 3 . (i) Find...
If A, B and C are arbitrary events of a sample space Ω, express A U B U C as the union of three disjoint events.
4·Let A and B be non-empty subsets of a space X. Prove that A U B is disconnected if A n B)U(A nB) 0. Prove that X is connected if and only if for every pair of non-empty subsets A and B of X such that X A U B we have (A B)U (An B)O.