(Note: Problem solutions are available at

1. Draw a state diagram for a microwave oven.

2. Convert the following state diagram to equations.

3. Implement the following state diagram with equations.

4. Given the following state diagram, use equations to implement ladder logic.

5. Convert the following state diagram to logic using equations.

6. You have been asked to program a PLC that is controlling a handicapped access door opener. The client has provided the electrical wiring diagram below to show how the PLC inputs and outputs have been wired. Button A is located inside and button B is located outside. When either button is pushed the motor will be turned on to open the door. The motor is to be kept on for a total of 15 seconds to allow the person to enter. After the motor is turned off the door will fall closed. In the event that somebody gets caught in the door the thermal relay will go off, and the motor should be turned off. After 20,000 cycles the door should stop working and the light should go on to indicate that maintenance is required.


a) Develop a state diagram for the control of the door.

b) Convert the state diagram to ladder logic. (list the input and the output addresses first)

c) Convert the state diagram to delayed update equations.

7. Design a garage door controller using a) block logic, and b) state-transition equations. The behavior of the garage door controller is as follows,

- there is a single button in the garage, and a single button remote control.

- when the button is pushed the door will move up or down.

- if the button is pushed once while moving, the door will stop, a second push will start motion again in the opposite direction.

- there are top/bottom limit switches to stop the motion of the door.

- there is a light beam across the bottom of the door. If the beam is cut while the door is closing the door will stop and reverse.

- there is a garage light that will be on for 5 minutes after the door opens or closes.

8. Convert the following ladder logic to delayed update equations and then draw the state diagram for the system. Is something missing from the system?

9. A program is to perform the following actions for a self-service security check. The device will allow bags to be inserted to the test chamber through an entrance door. If the bag passes the check it can be removed through an exit door, otherwise an alarm is sounded. Create a state diagram using the steps below.

1. The machine starts in an ‘idle’ state. The ‘open_entry’ output is activated to open the input door. The ‘open_exit’ output is deactivated to close the output door.

2. When a bag is inserted the ‘bag_detected’ input goes high. The ‘open_entry’ output should be deactivated to close the door.

3. When the ‘entry_door_closed’ and ‘exit_door_closed’ inputs are active then a ‘test’ output will be set high to start a scan of the bags.

4. When the scan of the bags is complete a ‘scan_done’ input is set. The ‘test’ output should be turned off.

5. The scan results in two real values ‘nitrates’ and ‘mass’. The calculation below is performed. If the ‘risk’ is below 0.3, or above 23.5, then the machine enters an alarm state (step 8), otherwise it continues to step 6.

6. The ‘open_exit’ output is activated to open the exit door. The machine waits until the ‘bag_detected’ input goes low.

7. The ‘open_exit’ output is deactivated to close the door. The machine waits until the ‘exit_door_closed’ input is high before returning to the ‘idle state.

8. In the alarm state an operator input ‘key’ must be active to open the exit door. After this input is released the door will close and return to the ‘idle’ state.

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