5 For a system: Y() 10.4s? +47s +160 U(s) 5+148° +568 +160 use Matlab to do: (a) obtain the state-space representation of the system. (b) transfer the state-space representation into Modal canonical form. (c) find the eigenvalues of the system matrix A, determine the system stability (d) find the controllability and observability matrixes. Determine the controllability and observability.
i dont understand this problem. please show how to solve all
parts using MATLAB. thank you.
State-Space Representation and Analysis csys canon(sys,type) compute a canonical state-space realization type 'companion': controllable canonical form type modal: modal canonical form poles of a system controllability matrix observability matrix eig(A) ctrb(A,B) obsv(A,C) -7 L-12 0 EX A 2C-ioD0 uestions () Define the system in the state-space form (2) Determine the stability of the system (3) Determine the controllability and the observability of the system....
I. Obtain a state-space equation and output equation for the system defined by: Y(s) US 233 + 32 + s + 2 $3 + 4s2 + 5s + 2 II. Obtain the transfer function of the system defined by [$][:13]• [1] III. Check the controllability and the observability for the system in branch II
A) For the schematic above find the state-space equations that
define this system.
B) Using the controllability rank test determine if this system
is controllable.
C) Using the observability rank test determine if this system is
observable.
1. Controllability and Observability L = 100 m R1 = 10 Ohms Mm R2 = 100 Ohms R4 = 100 Ohms ( = 100 microfarads ult) 1V R3 = 100 Ohms R5 = 100 Ohms Xı = i(t) y = valt) vi(t) =...
14.01. Find H(s) = I(s)/Vs(s), and the forced response i(t) for us =sin 2t V. For what range of a does this corre- spond to the steady-state response? Explain. 282 14 H () 00 av, κυ, PROBLEM P14.61 1421. Find H(s) = I(s)/Ig(s) and put in standard form. Specify all break frequencies. 312 iD PROBLEM P14.21 114_11. Find the forced response v(t). For what range of the controlled source gain r does this correspond to the steady-state response? Explain. 1H...
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54 +52 +7 Convert the following state space into a transfer function. (Marks 5) x = 11 * = x + ( u 21 y = [02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) i [ 10] [21. *= 15 2]* +11 y = [ 02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) -1 0x+lu x =...
Consider a modification of the RC filter that we discussed in class, where we additionally use an inductor L > 0 in the circuit. The governing system of equations is given by LC(d2v/ dt2(t)) + RC(dv/dt (t)) + v(t) = u(t), where u us the input voltage, t ∈ T ⊂ R, L, C, R > 0, and v is the output voltage. Provide answers to the followings:(i) Find the output v in terms of u (take the initial conditions...
(2) Let S be the surface parametrized by r(u, v) = (u? – 12)i + (u + v)j + (u? + 3v)k. (a) Find a normal vector to S at the point (3,1,1). (b) Find an equation of the tangent plane to S at (3, 1, 1).
Exercise 4.5.3. Let G-(g g 1 be a group of order 2 and V a CG-module of Let u +202 +2,u2 2v1 - 2 +2vs,u vector space spanned by ui, for i-1,2,3 2v - 202 +vs, and hence U the (i) Prove that U is a CG-submodule of V fori 1,2,3, and that (ii) Let λ C and u-ul + U2 + λν3 V. Find the value(s) of λ for which the subspace U spanned by u is a CG-submodule...
The simulink part can be neglected as I can manage. Just need
the mathematical solution for all the parts (specially part f)
Q2) The input-output relationship of a linear system is given by y(t) + 250y = 50u(t) a) Simulate the step response of the above system using Simulink. Comment on the figure obtained. (5 marks) b) Give a state space representation of the above system. (5 marks) c) Give a discrete-time representation of the above system using a zero-order...