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Process Control Example 1

    Heating, Ventilation, and Air Conditioning (HVAC) System

  • This is a simple HVAC system that is composed of the above three components: valve, pump, and controller.
    • Valve
      • Events: Stuck_closed_1 (SC1), Stuck_closed_2 (SC2), Stuck_open_1 (SO1), and Stuck_open_2 (SO2), Open_valve and Close_valve.
      • States: Stuck Closed (SC), Stuck Open (SO), Normal Valve Closure (VC), Normal Valve Open (VO).

      • The valve consists of four failure events that are unobservable. In this model, there are two valves: valve 1 and valve 2, each of which have two failure states. The failure events take place when either valve becomes stuck closed, and when either valve becomes stuck open.

    • Pump
      • Events: Pump_failed_off_1 (PFOFF1), Pump_failed_off_2 (PFOFF2), Pump_failed_on_1 (PFON1), Pump_failed_on_2 (PFON2), Start_pump, Stop_pump.
      • States: Pump Off (POFF), Pump On (PON), Pump Failure Off (PFOFF), Pump Failure On (PFON).

      • This system has two pumps: pump 1 and pump 2, each of which have two failure events that are also unobservable. They take place when either pump 1 or 2 fail to turn off, when they are already turned on, or fail to turn on, when they are already turned off.

    • Controller
      • Events: Open_valve, Close_valve, Start_pump, Stop_pump
      • States: C1, C2, C3, C4

      • The controller has no failure events.

  • Parallel Composition of Pump-Valve-Controller

  • In order to model the overall behavior of the system, we perform a parallel composition of the three components. The dotted lines represent unobservable events and the solid lines represent observable events.

  • Sensors

  • For the purpose of fault detection, we should add two sensors, one pressure sensor on the pump, and a flow sensor on the valve. We now have two sets:
    Y1 = {NP, PP} for the pump's pressure (NP is no pressure, PP is positive pressure)
    Y2 = {NF, F} for the valve's flow sensor (NF is no flow, and F is flow).
    Below is the corresponding Global Sensor Map.

    The map h is defined only for the accessible states of our overall system. The dots also indicate that there is no dependence on the controller states.

    The new sensor states will be denoted by a filled in solid circle instead of a open white circle. The dotted events are still representative of unobservable events and the solid ones are observable.

  • For more information on this example:
    Sampath, M., Sengupta, R., Lafortune, S., et. al. "Failure Diagnosis Using Discrete-Event Models." IEEE Transactions on Control Systems Technology. 4.2(1996): 105-124.
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