Properties of Open-Loop Controllers

Two most common tasks in controller design is regulation and signal tracking. Regulating controllers try to keep system stably in a fixed state. Balancing an inverted pendulum or keeping the speed a car at constant level are most obvious examples of regulation problems. All kinds of servomechanisms, such as autopilots and robotic arms, are the examples of signal tracking problems. An open-loop controller is a controller that does not use any feedback from a systems. For obvious reasons, open-loop controllers can be used only for signaltracking tasks. If we can keep a system in a desired state without measuring the system state, there is no reason to build a controller—we can just hardwire the corresponding inputs into the system. As there is no feedback in open-loop controllers, we can always assume that the system output y is a set of signals or internal states that we want to control. For instance, we might want to control the position (measurable output) and speed (internal state) of a car. Any open-loop control task can be formalised as follows. Design a controller that transfers a reference signal r to an input signal u such that the output signal u tracks the reference signal as closely as possible: