Modern Control System Theory and Design, 2nd Edition

ANSWERS TO SELECTEDPROBLEMS

CHAPTER 1

1.1. An electrical signal proportional to the difference between the desired heading (gyroscopic setting) and original heading is amplified by the power amplifier. The amplified signal drives the motor which turns the rudder until the desired heading and actual heading of the ship are in agreement, and the corresponding electrical signal that is proportional to the difference between these two headings is zero. This is an open-loop control system as there is no feedback signal.

1.2. The rudder’s positioning can be made into a closed-loop control system by fastening a resistor to the rudder in a similar manner to the resistor that is fixed to the ship’s frame. An electrical feedback signal can then be obtained of the actual position, which can be appropriately compared with that of the desired, or reference, position.

1.3. If the reference temperature of the thermostat is changed, the reference input to the control system changes, and an electrical error signal resuls. The electric hot-water heater will then change the temperature of the water until the difference between the reference input and actual temperatures is zero.

1.4. A change in the ambient temperature surrounding the tank manifests itself as a disturbance input within the heating control system. The explanation of the system’s resulting control action is similar to that discussed in the book for a disturbance occurring in an automatic speed-control system (see Figure 1.10).

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