CONTROLS 2 Consider the transfer function V (s) Put the system in state space form. Compute the eigenvalues of the resulting A matrix. Is the system stable? 2 Consider the transfer function V (s...
CONVERT FROM TRANSFER FUNCTION FORM TO STATE SPACE FORM AND COMPUTE THE EIGENVALUES AND EIGENVECTORS Y(s) U(s) ー0.0 1785G3 +77.88 +0.496s +0.446) (s2 +0.00466s +0.0053)(s2+0.806s+1.311)
Consider a single input, single output system with transfer function 10 H(s)- s+10s +25s +100 Obtain a state-space model in observer canonical form for the system, and design a full state estimator for desired eigenvalues of -10.-20 and-30. What are the values of the estimator gain matrix? Consider a single input, single output system with transfer function 10 H(s)- s+10s +25s +100 Obtain a state-space model in observer canonical form for the system, and design a full state estimator for...
8.5 Consider a system with transfer function ĝ(s) = (s – 1)(s+2) (s + 1)(s – 2)(s +3) Is it possible to change the transfer function to S-1 8f(s) =_ (s + 2)(s +3) by state feedback? Is the resulting system BIBO stable? asymptotically stable?
Problem 4. Transfer function to state space form Find the state-space form of the following transfer func- tions (see Section 4.4.1 in the book). This requires zero computation, it just requires you understand how a SISO transfer function relates to the state space form shown in the book. a) = Y(s) _ 68 +3 G(s) s3 + 26s2 5s 50 b) Y(s) + 2s2 + 4s 6 U(s) s3 +12s +12
2. Find the state space representation of the system represented by the following transfer function: (s +1.2) (s 15.8) (s +23) s(S 1.3) (s +7.2) (s + 47) G(s)- 3. Find the transfer function of the system with the following state space representation: 1 3.2 1.6 1(01) [-1 e) -7.4 2.4 -9.1l(O You may use your calculator, Matlab, or calculate by hand to find the following transfer functions: G1(s) 0,() R(S) G3(s) s) R(
Problem 1. Consider the following transfer matrix s+1 T(S) = Let G=TO -6-s s+1 Find the eigenvalues and eigenvectors of G Problem 2. 1. Show that the following push-through rule is valid. K(I - G2K1) -1 = (1 - K;G2) -'K, 1. What is the transfer matrix G, from d and n 2. In the following system, let C(s) = -- and P to z? 3. A MIMO system is given by (x = u - 2x₂ + x2 x2...
PROBLEM 1 Consider the transfer function T(S) =s5 +2s4 + 2s3 + 4s2 + s + 2 a) Using the Routh-Hurwitz method, determine whether the system is stable. If it is not stable, how many poles are in the right-half plane? b) Using MATLAB, compute the poles of T(s) and verify the result in part a) c) Plot the unit step response and discuss the results. (Report should include: Code, Figure 1.Unit step response, answers and conclusion) PROBLEM 1 Consider...
1. If the ax matrix A has eigenvalues ....., what are the eigenvalues of a) 4*, where & is a positive integer. AE? A ' b) ', assuming the inverse matrix exists. c) A' (transpose of ). d) a, where a is a real number. e) Is there any relationship between the eigenvalues of 'A and those of the A matrix? Hint: Use to justify your answer. 2. Compute the spectral norm of 0 0 b) c) c) 1-1 0...
4.22. Consider the vibrating system described by 42 -2 1 Compute the mass-normalized stiffness matrix, the eigenvalues, the normalized eigen- vectors, the matrix P, and show that PTMP I and PTKP is the diaggaal matrix of eigenvalues Л 4.22. Consider the vibrating system described by 42 -2 1 Compute the mass-normalized stiffness matrix, the eigenvalues, the normalized eigen- vectors, the matrix P, and show that PTMP I and PTKP is the diaggaal matrix of eigenvalues Л
Consider an LTI system for which the system (transfer) function H(s) has a zero at s=2 and poles at s=-12, -7, -6. If the system is known to be causal and stable, choose the ROC associated with the given system function. *