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
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- 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.a. For the translational mechanical system shown in Figure (3). 1. Write the mathematical model in a format of matrices. 2. Find the transfer function G(s) = a₁ (s)/T (s) where a is the acceleration. t 45²² +16,5 245+628²-2-05+96 M₁ = 8 kg 6 N-s/m f(t) 1 N/m 0000 4 N-s/m -x₂(1) M₂-3kg Frictionless 0000 15 N/m Frictionless Figure (3) Translational mechanical systemFigure 1 shows an electrical system comprising a series RLC circuit and input voltagesource ein(t).(a) Derive the input-output equation with output y = I and input u = ein(t). (b) Using the derived input-output equation, drive the system transfer function G(s)that relates output to input. Use the following numerical values for the electrical systemparameters: resistance R = 2Ω, inductance L = 0.25H, and capacitance C = 0.4F. (c) Using the derived transfer function, derive the time-domain ordinary differentialequation for the input-output equation of this electrical system. (d) Draw the complete block diagram of this series RLC circuit using the derived transferfunction.
- 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/sA common actuator in control systems is the DC motor. It directly provides rotary motion and, coupled with wheels or drums and cables, can provide transitional motion. The electric circuit of the armature and the free body diagram of the rotor are shown in figure 3. Determine the following. i. The differential equations from the electrical circuit and the mechanical part. ii. Convert the differential equations to state space representation. The output is the speed of the de motor dt ii. Given component values R=5 Ohms, L= 6H, J= 8 kg-m?, b=4 N-m s/rad, assuming back Emf constant and motor torque constant are equal Kb=Kt=K=10, determine its controllability of the DC motor. iv. Based on the performance of the DC motor, recommend at least 3 ways on how to increase it angular velocity, and justify your answer. Fixed field R L Armature circuit indows bui انتقل إلى الإعدادت Rotor Figure 3what is the closed loop transfer function K Кр 1+ Ts
- Q1 Consider the system shown below. R- R/27 m T y Moment of inertia of the drum is equal to I. +y + direction Obtain the state space representation of the system given the output is the displacement y. (P4)1. The equations of motion of this system are ÿ + 3y + 4y - 32 - 4Z = 0 Ż +52 +6Z-5ý - 6y = f(t) * = A + Bū y = Cx+Dū Put these equations into state variable form and express the model as a matrix vector equation if output of the system is y. Energy storage element m1 m2 k₁ k₂ State variable *1=ý x₂ = Ż x3 = y x4 =Z k₁ my D k₂ C₂H m₂03/A heating system shown in figure 1; the mathematical model of this system is written as: Ct, = q - 41 C†2 = 91 - 92 Here 91 = T-T2 91 = R1 T-To R2 Derive the transfer funetion for the system assuming q, is the input and q; is the output, and then draw the block diagram which describes the system graphically. Hint: C, C2, R1. Rz are constants. T. Outside Air inside the oven 92 R2 Figure I T
- A satellite single-axis amplitude control system can be represented by the block diagram is as shown in Figure 2.11. The variable k, a and b are controller parameters, andj is the spacecraft moment of inertia. Suppose the moment of inertia is J=7.8E+08 (slug-ft), and the controller parameters are k=10.8E+08, a=1.5 and b=8. Spacecraft Rotational R(s) Controller motion C(s) k(s + a) (s + b) js? Figure 2.11 A negative feedback control system a) Develop an m-file script to compute the closed loop transfer function. b) Compute and plot the step response to a 10° step input. c) The exact moment of inertia is generally unknown and any change slowly with time. Compare the step response performance of the spacecraft when J is reduced by 25% and 60%.Figure 3 Q.6/ For the system shown in Figure 4, a step torque is applied at 0,(t). Find a. The transfer function, G(s) = 02(s)/T(s). b. The percent overshoot, settling time, and peak time for 02(t). [Section: 4.6] T(t) 0,(1) 02(1) ff 1.07 kg-m2 1.53 N-m-s/rad 1.92 N-m/radFor the mechanical translation system below, find the force-voltage analogy and force-current analogy. Use the following values. K1 = 2 fv, = 1/2 M1 = 1+a %3D K2 = 2 fv2 = 4+b M2 = 5 K3 = 3+c fv3 = 3 a = 0 where a = 3rd digit of your student number %3D 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.