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42. Solve the following state equation and output equation for y(t), where u(t) is the unit step. Use the Laplace transform method. [Section: 4.10]
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Chapter 4 Solutions
Control Systems Engineering
- A mechanical system is described by the following transfer function -4s H(s) = sª-2s² + s-17 If u is the input, and y the output, Cast this system into the state variable format. (Do not find the solution for the system) Yarrow_forwardA crane hoisting system has the following transfer function. 1 s4 +5s3+s² + 7s+ 11 +s²+7s+ Identify the correct state-space form of the crane hoisting system from the list given below: 100T O a. 0 0 x = 0 -11 O b. x = = -5 1000 00 1 0 x + 01 1 5 1000 1 0700 0070 -1 -7 [−11 1 u; y = [1000]x x + u; y = [1_0_0 0]x 1111 ○ c. 0 1 0 0 0 0 1 0 x = + 0 0 0 1 -11 -7 -1 -5] O d. None of the above u; y = [1 0 0 0]x 2512220 12arrow_forwardQ3 A mass-spring-damper (MSD) system is modelled by the transfer function Gp(s) = 1 s² + 2s +3 The control system is designed to control the MSD system described in figure 1, where U(s) is the reference input and C(s) is the displacement of the object. (a) Use Matlab and block reduction techniques to determine the closed loop transfer function C(s)/U(s). [20 Marks] (b) Plot the unit step response of the system output.arrow_forward
- For the mechanical translation system below, find the transfer function 0,/T and O2/T. Use the following values. K = 1+c D1 = 1 Jj = 4+a J2 = 3+b D2 = 5 where a = 3rd digit of your student number %3D = 7 = 5 b = 5th digit of your student number c = 7th digit of your student number For reference, the 1st digit of your student number is the leftmost number in your student number. Indicate your student number when solving problems. T(t) 0(t) 02(1), elel J2 D1 K D2 ON II ||||arrow_forwardFor the following state-space representation,define the:– State Vector– System Matrix– Feedforward Matrix– Input Matrix & Input Vector– Output Matrix & Output Vectorarrow_forwardExplain the state space functionarrow_forward
- can i get help for B only.arrow_forwardRequired information Use the following transfer functions to find the steady-state response yss() to the given input function f(t). NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. T(-) Y(s) F(s) s(e) 10 b. = 9 sin 2t s²(s+1) ' The steady-state response for the given function is yss() = | sin(2t + 2.0344).arrow_forwarda) Suspension system of a car. Finding the transfer function F₁(s) = Y(s)/R(t) and F₂ (s) = Q(s)/R(t), consider the initial conditions equal to zero. car chassis www K₂ M₂ 1 Tire M₁ K₁ B₁ y(t)= output q(t) r(t)= input Where [r, q, y] are positions, [k1, k2] are spring constants. [B₁] coefficient of viscous friction, [M₁, M₂] masses. b) Find the answer in time q(t) of the previous system. With the following Ns values: M₁ = 1 kg, M₂ = 0 kg, k₁ = 4 N/m, k₂ = 0 N/m, B₁. = 1 Ns/m, considered m a unit step input, that is, U(s) = 1/sarrow_forward
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