Homework 2-merged

1. Find the transfer function. A = [² = ₁], B = [1] . C = [0_1], D = F2] SEST-AT Y(s) U(s) = C[sl-A] B+D X = AY + Bui V = Cx + Du

dont do the simscape piece

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?

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

Please solve the following by hand and without the use of AI. Thank you!

A servo motor system has the following state-space model -2 91 * = [² } ] x + ||] u; 3] x + [1] u; y = [09]x 3. Find the transfer function equivalent for the motor system from the following: 9s a. s²+2s+9 O b. 9+s s²+25+9 ○ C. 9 s²+2s+9 ○ d. None of the above

Q3 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.

a) 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/s

Q.4- A model for feedback control system employing both angular position and velocity feedback is shown in figure bellow .The equation describing d²0 do di the system is J di² - = • K.[V₁-K₁0. K₂0-Ka ((1) Summing V,(r) Motor 白口食 amplifier Velocity sensor K₂8 Position sensor Where J is the rotary inertia KandK are the position and velocity feedback gains, and K, is the gain between the input voltages to the motor torque produced. Derive expression for the closed loop system undamped natural frequency and damping ratio.

The simplified robot arm model is given in the following: * = [5 -5 x + |u; y = [03]x 1 Is the system defining the robot arm model observable? O a. Yes O b. No ○ c. Not possible to determine Od. None of the above

Figure 1 shows a six degree of freedom industrial robot. i. Construct the coordinates frames based on the D-H representations. ii. Complete the D-H parameter as illustrated in Table 1.

Do not give answer in image and hand writing

Please solve the following by hand and without the use of AI. I am working to understand the step by step procedure of solving this problem so pleaase give a detailed step by step procedure, explaining each part as you go. Thank you!

Please solve the following by hand and without the use of AI. I am working to understand the step by step procedure of solving this problem so pleaase give a detailed step by step procedure, explaining each part as you go. Thank you!

Need help solving this problem. Please provide clear and concise steps.

Q1. A mechanical system is shown in the following figure, where external force u₁ is the input and displacement y₂ is the output. The force acting on m₂ has a linear relationship with u₁ as u₂-Au₁. • List system equations and do Laplace transform to the system equations; • Draw block diagram of the control system. (Please construct the block diagram from system equations directly, do not derive or combine the equations. Do not need to reduce it) YI Y b₁ m₁ 11 112 + m₂ www

21. The programmer uses three-point method for UT[2] setup for a sharp-tip pointer. If the programmer recorded each of three-points by precisely contacting the sharp-tip to the tip of the stationary reference pointer on the table, then (a) UT[2] setup is accurate (b) UT[2] setup is not accurate (c) the accuracy of UT[2] setup is still uncertain 22. User frame UF[3] is accurately set up on the part reference surface which is unparallel to the surface where the robot is mounted. To jog the robot TCP to move perpendicularly to the part reference surface, the programmer (a) needs to select World jogging coordinate system (b) needs to activate UF[3] and select User Frame jogging coordinate system

Given the trasnfer function G(s) numerator and denominator coefficients for Matlab code should be: O s³+2s+1 2s4+2s²+1' the num= [1 0 2 1] and den=[2 020 1] O num=[1 2 1] and den=[2 0 2 1 1] O num=[1 2 1] and den=[2 2 1] O num=[1 0 2 1] and den=[2 2 0 1]

A servo motor system has the following state-space model x = [+² -2 9 1 3. x+]u; y = [09]x Find the transfer function equivalent for the motor system from the following: 9s a. s²+2s+9 O b. 9+s d. s²+2s+9 9 s²+2s+9 None of the above