Real Time Application

Digital Controller

Many real-time systems are embedded in sensors and actuators and function as digital controllers. Figure, below shows such a system. The term plant in the block diagram refers to a controlled system. An engine, a brake, an aircraft, a patient are some examples. The state of the plant is monitored by sensors and can be changed by actuators. The real-time system estimates from the sensor readings the current state of the plant and computes a control output based on the difference between the current state and the desired state (called reference input shown in the figure). This computation is called the control-law computation of the controller. The output generated activates the actuators, which bring the plant closer to the desired state.

A simple example is shown below: consider an analog single-input/single-output PID (Proportional, Integral, and Derivative) controller. This simple kind of controller is commonly used in practice. The analog sensor reading y(t) gives the measured state of the plant at time t. Also, let e(t) = r(t)− y(t) denote the difference between the desired state r(t) and the measured state y(t) at time t. The output u(t) of the controller consists of three terms: a term that is proportional to e(t), a term that is proportional to the integral of e(t) and a term that is proportional to the derivative of e(t). (Liu 2)

High-level Controls

The controllers in a complex monitor and control system are often organized in a hierarchy. There can be multiple control loops and the high-level controller interfaces with the operator and monitors the behavior of low-level controllers. The output of high-level controller acts as the reference input of low-level controller. The time scale and the complexity of decision making increases as we group the hierarchy. One or more low-level digital controller directly control the physical plant. The periods of low-level control law computation is millisecond to second level and is simple while the periods of high-level control can be from few minutes to many and is complex. When we move from low level to high level, the system moves from direct control to the planning.

Guidance and Control

While a digital controller deals with some dynamical behavior of the physical plant, a second level controller typically performs guidance and path planning functions to achieve a higher level goal. In particular, it tries to find one of the most desirable trajectories among all trajectories that meet the constraints of the system. The trajectory is most desirable because it optimizes some cost function. The algorithm used for this purpose is the solution of some constrained optimization problem.

For an example, look again at a flight management system. The constraints that must be satisfied by the chosen flight path include the ones imposed by the characteristics of the aircraft, such as the maximum and minimum allowed cruise speeds and decent/accent rates, as well as constraints imposed by external factors, such as the ground track and altitude profile specified by the ATC system and weather conditions. A cost function is fuel consumption: A most desirable flight path is a most fuel efficient among all paths that meet all the constraints and will bring the aircraft to the next metering fix at the assigned arrival time. This problem is known as the constrained fixed-time, minimum-fuel problem. When the flight is late, the flight management system may try to bring the aircraft to the next metering fix in the shortest time. In that case, it will use an algorithm that solves the time-optimal problem.

Real-Time Command and Control

The controller at the highest level of control hierarchy is called command and control. For example, air traffic control (ATC) system architecture shown in the figure monitors the air crafts in its coverage environment and generates and provides the information needed by the operator. The output information from ATC system includes the assigned arrival times to the metering fixes and these inputs acts as on board flight management system called physical plant. Therefore, the ATC system indirectly controls the embedded components of low levels of control hierarchy. Similarly, the ATC system provides voice and telemetry services to onboard avionics. Therefore, the commands and control fascinates both high level and low-level control.

The ATC System collects information about the state of the aircrafts through the sensors of radars. The state variables include identifier, position, altitude, heading, distance, speed and so on. These variable collectively are called track record and the current trajectory of the aircraft is a track. The information collected is processed by the DSPs and is stored in the database. The stored data is further processed by DPs and displayed by the display on. The surveillance system continuously analyzes the scenario and alerts the operator whenever it detects any potential hazards.

References

Liu, Jane W. S. Real Time Systems. Integre Technical Publishing Co., Inc, January 10, 2000. Print.