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

The ratio of output to input of a system is known as Transfer function. Select one: O True O False Coloct the cinmple cuctom fcom the fellouuing

200 OOOD O Subject Date: Q1/Find the domain P the function 2. Y3DIn(2x+X-6-6)

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) Y

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

For the mechanical translation system below, find the transfer function X2/F and X1/F. Use the following values. K =1 fv = 1 M, = 4+a K2= 1/2 fv2 = 3+b M2 = 5 K3 = 1+c fv3 = 3/2 where a = 3rd digit of your student number %3D b = 5th digit of your student number %3D 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.

10- To enter the transfer functions G(s)= a) G= th(2, [3,2]) b) c) d) G(s) TH (2, [2, 3]) G= tf (2, [3,2]) G(s)= TF(2, [2, 3]) 2 3s+2 c) A marginally stable response d) A marginally unstable response to Matlab command use: 3s+1 11- To enter the transfer function g(s)= $2+35+2 ,can be use a) num=[3, 1]; den= [1, 3, 2]; g-tf (den, num) num=[3, 1]; den=[1, 3, 2]; g=tf (num, den) b) c) num=[3; 1]; den=[1, 3, 2]; g=tf (den, num) d) num=(3, 1); den=(1, 3; 2); g-tf (num, den) 12- What is the output of the code (>>p=[0 1]; q=[ 1 -1 0]; step(p,q) ) a) An unstable response b) A stable response (s+1)

For the mechanical translation system below, find the transfer function 01/T and 02/T. Use the following values. K = 3+c D1 = 1 J1 = 2+a J2 = 4+b D2 = 5 %3D where a = 3rd digit of your student number a =O b = 5th digit of your student number b = 7 c = 7th digit of your student number c = 5 For reference, the 1st digit of your student number is the leftmost number in your student number. Indicate your student number when solving problems. 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,(1) 02(1), D1 K D2

Write the system equations and the corresponding state-space representation or each of the systems given below. НІНІНІНІНІ K₁ 0000 M₂ K₂ M₂0000 M f(t) [

4. Consider a batch process of the conveyor oven illustrated in Figure 1. List all input and output process variables involved (binary and continuous), and draw the block diagram for the automation of the conveyor oven temperature and the connection schematic of the programmable logic control interface with process field devices. Motorized circulating fans Airflow (m/s) Electrical heating elements Heater voltage (volt) ww. Thermostat Thermostat ("C) ("C) 111111tt, Cake Cake Cake Cake Cake Cake II Travel direction Screw conveyor Stepping motor Figure 1: Cake conveyor oven.