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EEE8150
Industrial Automation, PLCs and Robotics

Time allowed - 2 hour

Instructions for candidates:

Candidates must answer ANY TWO questions from Section A and the ONE question from Section B.

All questions carry equal marks

[Marks shown for subsections are indicative only]

It is important to show the method of calculation and the steps taken to achieve the results.

Calculators are allowed.

This is a closed book exam; no additional notes are allowed.

SECTION A

Question 1

a) In the context of connecting a DC Input Module to a PLC, what is meant by the terms Sinking and Sourcing? Illustrate your answer with a diagram. [6 Marks]

b) Draw equivalent Ladder Logic Diagrams for the following logic gates. [6 Marks]

ii)

iii)

c) Give four advantages / disadvantages of using PLC Ladder Logic instead of Relay Logic in designing a complex control circuit. [4 Marks][EEE8150]

Figure 1

Disneyland Paris is creating a train ride that will travel around the attractions and allow people to get on and off at the platforms. They require you to create a RELAY control circuit for the train. The train only travels in one direction and stops at each platform for 60 seconds before moving on.

The train control unit has the following inputs: START button, STOP button, RESET button and PROXIMITY sensor.

The train control unit has the following outputs: MOTOR, SPEAKER, DOOR and BRAKE.

The train control circuit starts when the START is active and the RESET & STOP are de-active. The STOP button is an emergency stop and will require: the BRAKE to be applied instantly with the DOOR open and the MOTOR turned off.

Upon arriving at a Platform (or START is active) the train will wait at the Platform for 60 seconds. At the end of 60 seconds a SPEAKER is activated (a recorded message asking people to stand away from the train door). After another 10 seconds (time required for speaker message to finish) the BRAKE is turned off, DOOR is closed (turned off) and the MOTOR turned on.

At any platform the PROXIMITY sensor will be activated (and remain active till leaving the platform). When the PROXIMITY sensor is activated the MOTOR will be turned off and the BRAKE turned on and the DOOR should open (turned on). This whole process will repeat until the STOP or RESET is activated.

Question 2

Consider the Inverted Pendulum System shown in figure 2, consisting of a cart mass M with a freely swinging pendulum of mass m which you can consider to be effectively at the end of the pendulum length l A control force F is applied to the cart, which moves along the x axis.

The frictional force between the cart and the rails is acting in the opposite direction to the motion of the cart. The angle between the pendulum rod and the vertical is θ and the Rotational Inertia of the pendulum is I.

a) Show that the nonlinear equations that fully describe this system are

[18 Marks]

b) Linearise these equations for the case when the pendulum is close to the upright position, clearly explaining your methods. [6 Marks]

c) Discuss the Control Process and Problems associated with getting the inverted pendulum to swing up from the stable equilibrium rest position to the upright unstable equilibrium position. [6 Marks]

Question 3

a) Write the mathematical equation that describes the Boolean membership function and the Logic Membership function with reference to the universe of discourse “x” and the fuzzy set “A”. Then describe the main different between Boolean Logic and Fuzzy Logic. [7 Marks]

b) The discrete fuzzy sets A and B have a universe of discourse defined as the integers from 1 to 10. Their membership functions are described as follows:

Write down the sets . [5 Marks]

c) You are tasked to calculate the PID control values for a Plant control scheme using the Zeigler Nichols Open Loop Resonance tuning method. The figure 3 shows a unit step u(t) response being applied to the Plant which has an output of y(t). Show all your working out in calculating the closed loop controller PID values.

[8 marks]

d) Draw a control model applying your PID Controller values to a plant. [4 marks]

e) Figure 4 shows the simulated testing result after you have applied the PID values to your Controller (contained in part Question 3 Part c/d) and have applied an input reference demand of 100 rpm.

Describe the effects of increasing the controller gains on the response of the system and state what changes should be made to the controller to improve the performance.

Figure 4 [6 marks]

SECTION B

Question 4

a) Consider a robot which has the orientation of its end-effector with respect to its base frame described by the Roll Pitch Yaw orientation matrix

By considering the general form of the homogeneous transformation

i) Define what the general homogeneous transformation matrix is and identify the general translation matrix for the RPY. [5 Marks]

ii) Define the orientation matrix for:

[3 Marks]

iii) Derive expressions for θ, ψ and ψ in terms of entries of ^RT^H[6 Marks][

b) For the robot manipulator shown below in figure 5:

Figure 5

i) Generate a Link Table of this robotic manipulator [3 Marks]

ii) Derive the general transformation matrix [9 Marks]

iii) Given that l₁= l₂= 0.25m and θ₁= 45deg, θ₂= -90deg find the orientation of the end effector by applying this information to the general transformation matrix and extrapolating the Roll, Pitch and Yaw angles. [4 Marks]

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EEE8150 Industrial Automation, PLCs and Robotics