University of Saskatchewan
College of Engineering
Dept. of Mech. Engineering
ME 460.3 Final Exam
April 10, 2010
Time: 3 Hours
Close Book Exam.
Instructors: Chris Zhang
This exam consists of seven questions. Attempt all questions.
Question 1:
Explain the following concepts.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
[12]
Plant and control system (using example);
State variable X (using example);
Controller input I (using example);
Controller output Y (using example);
Discrete event control system;
Continuous time control system;
Work space of a robot;
Singularity of robot movement.
Question 2:
[8]
Describe the procedure of computing the torque on the motor given the payload on the endeffector for a six degree-of-freedom robot.
Question 3:
[10]
Explain the following concepts in the context of robot path planning. Figure 1 may be used for
your explanation.
(a) Path planning;
(b) The boundary conditions including their physical meaning used to determine the path
plan between the two points of A and B (Fig. 1);
(c) The boundary conditions that are sufficient to determine a fifth order polynomial
function for the path between A and B (Fig. 1).
1
B
A
Figure 1
Question 4:
Explain the following concepts in the context of discrete event control
(a)
(b)
(c)
(d)
(e)
(f)
State diagram (using example);
Boolean Logic Equation (using example);
Electrical Ladder Logic diagram (using example);
Software Ladder Logic diagram (using example);
Programmable logical controller (PLC);
Latching.
2
[20]
Question 5:
[10]
Describe the procedure for designing a logic controller system. You should address the state
diagram, the logic equation, ladder diagram, PLC, and their connections.
Question 6:
[30]
Figure 2 shows a bottle-filling operation system. There is a motor in the system. The motor
drives the conveyor system to transport the bottle to the right position. When the bottle arrives at
the right position, the motor should be switched off, to make the bottle rest so that the liquid can
be filled into the bottle. There is a photo-sensor (PS) detects whether the bottle is filled. Please
design a discrete logic controller for the bottle-filling operation illustrated in Fig. 2. The system
consists of the following physical entities:
-
Start and stop pushbuttons (to start and stop the whole system),
Proximity switch (to detect if the bottle arrives at the right position;
Level limit switch (to detect the level of the liquid in the tank system which delivers the
liquid to fill the bottle);
Input valve switch (to control the amount of liquid into the tank);
Output valve switch (to control the filling process);
Photo-sensor (to detect if a bottle is filled);
Motor switch;
Output valve switch.
Let:
PB1 for start pushbutton, (PB1=1) for the start pushbutton is pressed
PB2 for stop pushbutton, (PB2=1) for the stop pushbutton is pressed
LLS for the level limit switch, (LLS=1) for the level of the liquid over the desired
(LLS=0) for the level of the liquid below the desired
BPPS for the proximity switch, (BPPS=1) for a bottle to arrive in position
(BPPS=0) for a bottle not to arrive in position
PS for the photo-sensor, (PS=1) for the bottle filled
(PS=0) for the bottle unfilled
S1 for input valve,
(S1=1) for the input valve is on
(S1=0) for the input valve is off
S2 for output valve,
(S2=1) for the output valve is on
(S2=0) for the output valve is off
M for motor switch
(M=1) for the motor is on
(M=0) for the motor is off
The basic control problem can be described in the following:
(1) The process is turned on by pressing the start pushbutton button switch
(2) The process is turned off by pressing the stop pushbutton switch, where off also means that
conveyor motor is off.
(3) When the process is running:
3
-
When the LLS=0, the input valve must be energized;
After a bottle arrives in position, the output valve must be energized;
After a bottle is filled, the output valve must be de-energized;
The conveyor is on when a bottle is not in position and is off when a bottle is in position
and is being filled; and
- The filling of bottles is then required over and over again.
Please do the following:
(a)
(b)
(c)
(d)
(e)
(f)
Define controller input variables;
Define controller output variables;
Define the state variable of the system;
Develop the state diagram for all the state variables identified in (c);
Develop logic equations for all the state variables identified in (d); and
Develop a PLC implementation (i.e., software ladder diagram).
Question 7:
[10]
A product is manufactured by processing a part at six different machines. The parts are processed
in batches of 25. The operation time per part per machine is 6 min, and the setup time and
nonvalue-adding operation time per machine per batch is 2 hr, and 4 hr, respectively. There are
10 machines in the manufacturing plant that operates a total of 70 hr per week.
(a) Compute the MLT for production the first batch.
(b) Compute the maximum possible production rate in parts processed per machine per hour
(c) Compute the WIP.
4
+
+
+
K
Kvv
Kpp
K
Photo-sensor
Figure 2
-
THE END –
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