1. The equations of motion of this system areÿ + 3y + 4y - 32 - 4Z = 0Ż +52 +6Z-5ý - 6y = f(t)* = A + Būy = Cx+DūPut these equations into state variable form and express the model as a matrix vectorequation if output of the system is y.Energy storage elementm1m2k₁k₂State variable*1=ýx₂ = Żx3 = yx4 =Zk₁myDk₂ C₂Hm₂

Answered: ÿ + 3y + 4y - 3Ż - 4Z = 0 Ż +52 +6Z -…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The Johnson & Royce model of a distillation column is driven by the inputs of steam flow and its flow rate; the output measurement is the temperature change. The state-space model is given by: -2 x = [¯²¯¯¯7 | x + | | | u; y = [0_1]x - the system defining the model of the distillation column is a. Asymptotically stable O b. Unstable Oc. Marginally stable Od. Indeterminate in relation to its stability
Page 8/5 Q4: (M4) LE Velocity: V [km/hr] Wavelength: L [m] M k y(t) Model Height: H [m] The figure above shows a model of a person riding a unicycle that contains a spring under its seat. The spring constant is k = 10,600 N/m. Assume that damping is minimal, the wheel of the unicycle has no mass and is not a spring, the unicyle always stays perfectly upright, and the person is represented by a rigid mass M = kg. a) When the unicycle is being ridden at speed V = 10 km/hr over the sinusoidal bumpy terrain shown above, with bump spacing L=0.6 m and bump height H 0.05 m, what will be the steady-state peak-to-peak amplitude of the motion y(t) [m] of the person riding the unicycle? b) Recalculate the steady-state peak-to-peak amplitude of the motion for 2.5, 5, and 20 km/hr. Will the rider have difficulty reaching speeds above 5 km/hr?
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4- Represent the system shown in Figure P4 in state space where the output is OL(t). T(t) N₁ = 30 2 N-m/rad 3 N-m-s/rad oooo N-m/rad N3 = 10 farm FIGURE P4 10 N₂= 300 I▬▬▬▬▬▬▬▬ N4 = 100 200 N-m-s/rad
diagram, F, is the input force exerted on the cart by the voltage applied to the motor, m, is the mass of the cart. The encoder is used to keep track of the position of the cart on the track. Cart Encoder Mater March 7, 2023 Track X Figure 5: Free body diagram of the cart (ignoring friction) Using Figure 5 and basic Newtonian dynamics you can derive the equations governing the system. 3.3 Motor Dynamics The input to your system is actually a voltage to the cart's motor. Thus, you need to derive the dynamics of the system that converts the input voltage to the foren exertal on the cart. These are the dynamics of the motor. Figure 6 shows a diagram of the electrical components of the motor. Figure 6: Clasic armature circuit of a standard DC motor For this derivation of the motor dynamics we assume the following: • We disregard the motor inductance: IR, so we can use the approximation 0. • Perfect efficiency of the motor and gearbox: -- 1. The torque generated by the motor is proportional…
Below is an open loop transfer function which is given: A(s) A(s) = = 0.1(s +14) (s+7)(s + 5) Use matlab's bode function and plot its bode diagram. Show the figure Use the following MATLAB script and write a code for bode plotting concerning the open loop transfer function. Clear Close all clc w 0. 1:0.001:100; ns = length (w); for i=1:nS %Write the code here end
A 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 12
6 Problem Compute the inverse Laplace transform f(t) = L−¹[F(s)] of the following function: s+1 s² + 6s +9 F(s) =
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If a system, * + 10x + 21x = 4f(t) is converted into a state-space model, what would be the state (A), input (B), and output (C) matrices? [where input = f (t) and output = x(t)] %3D A) A = | [-21 l, B = | and C = [0 1] В -10 1 B) A = 21 ol, B = and C = [1 0] %3D C) A = = Al and C = [1 0] В %3D -21 D) None of the above
Use MATLAB to obtain a state model for the following equations; obtain the expressions for the matrices A, B, C, and D. In both cases, the input is f(t); the output: is y. a. 5d³yd²y +7. b. dy +3 dt³ dt² dt Y(s) 5 = F(s) s² +7s+4 - +6y=f(t)
dont do the simscape piece

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