R(s)+E₁(s)environment(a)ControllerKps + K₁SPlant1(s + 1)(0.5s + 1)(b)WY(s) A mobile robot using a vision system as the measurement device is shown in the figure below. Thecontrol system is shown in figure (b). Design the controller so that(a) the percent overshoot for a step input is P.O. < 5(b) the settling time (with a 2% criterion) is Ts < 6s(c) the system velocity error constant Kv < 0.9(d) the peak time, TP, for a step input is minimized.Motion subsystemBObjectenvironmentRecognitionsubsystemComputer

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Answered: R(s) + E₁(s) environment (a) Controller…

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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2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)
1) Consider the system below: Vehicle Controller Steering dynamics Desired Actual bearing angle bearing angle 50 1 K s2 + 10s + 50 s(s + 5) Figure 1: Simplified Block Diagram of a Self-Guiding Vehicle's Bearing Angle Control. • Find a K value that the system has minimum rise time and minimum overshoot. Let us call this proportional gain as Kopt Show each step while finding Kopt- Show the necessary graphical solutions. Simulate the system response with 3 different K values. (Kopt and two other K values close to Kopt) Show the system response (actual bearing angle) in a single graph for different K values. • Comment on the results.
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 Use your knowledge of differentiation to sketch the velocity-time graph, clearly marking the critical points. Using the graph sketched in (a) above, estimate the velocity when t = 1.5 s Calculate the velocity of the function when t = 1.5 s by substituting to the velocity function. Compare this value to the value you estimated in b above.
(c) An electronic Pl temperature controller has an output p of 15 mA when the set point equals the nominal process temperature. The controller response to step change in the temperature set point of 3 mA is shown below. t(s) 0- 0+ 20 60 80 Determine the controller gain K, and the integral time.r p (mA) 8,0 6,8 6.0 4.4 3.6
Graph/Plot the output step response from t=0 to t=10 with a 0.1-second interval.
Match the transfer function with correct Bode phase plots. G(s) = 5 $+7 G(s)=s+5 G(s) = s+10 S S G(s) = S+ 10 QUESTION 10 90 deg 00 0 deg -90 deg 180 deg B. D 90 deg @ 0 deg -90 deg 180 deg 90 deg @ 0 deg -90 deg 180 deg 90 deg @ 0 deg -90 deg 180 deg
Using the following lines, let us create a virtual data concerning the joint torque (Nm) and angular velocity (RPM) of an imaginary actuator system: Kx = 29; Kn 200; dt 0.001; %sampling time 10; simulation time Ts ns Ts/dt +1; for i = 1:nS t(i) tau (i) = (i-1) *dt; time variable Kx*sin (2*pi*0.5*t (i)) + = 0.1*sin (2*pi*50*t (i)); dq (i) = Kn*cos (2*pi*0.5*t (i))*9.24; SOME CALCULATONS HERE end & THEN SOME OTHE CALCULATIONS HERE Calculate the average torque T_avg. Then referring the Harmonic Drive Catalogue, choose a gear model with a gear ratio of 1:30 in accordance with the T_avg value you calculated. Explain the rationale behind your choice.
An object was dropped off the top of a building. The function f(x) = -16x2 + 144 represents the height of the object above the ground, in feet, x seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function. f(-3) =___ meaning that___ seconds after the object was dropped, the object was___ feet above the ground. This interpretation___in the context of the problem. f(0.5)=___ meaning that___ seconds after the object was dropped, the object was___ feet above the ground. This interpretation____in the context of the problem. f(8)=___ meaning that___ seconds after the object was dropped, the object was___ feet above the ground. This interpretation___in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is___
You are tasked to enhance the performance of an analog plant using a digital controller PID. The controller is in connected in series with the plant in a closed-loop configuration. The pulse transfer K(z+a) function is given as GzohGp(s) =- Use sampling time Ts=0.6 second, K=8, a=0.78, b=-0.602 (0+z)(q+z) and c=-0.705. Do the following: i. Obtain the design point in z-coordinates to achieve the requirement of having a system settling time of 3 second, and damping ratio of zeta (z=0.705).
A stepper motor serves as the drive unit for the linear joint of an industrial robot. The joint Q4 must have an accuracy of 0.25 mm. The motor is attached to a leadscrew through a 2:1 gear reduction (2 turns of the motor for 1 turn of the leadscrew). The pitch of the leadscrew is 5.0 mm. The mechanical errors in the system (due to backlash of the leadscrew and the gear reducer) can be represented by a normal distribution with standard deviation = +0.05 mm. Specify the number of step angles that the motor must have in order to meet the accuracy requirement.
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.

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