Glossary of Control Related Terms

Preamble:
Here are a few definitions or descriptions of terms in control engineering; some of which might represent interesting perspectives, not conforming to the common or conventional view (Hence consider them Beta). More than one description or definition may be presented of the same word or phrase. And there may be additional ‘useful’ comments.

Words in the glossary:
Algorithms, Automation, Control Engineering, Control System, Cyber-physical Systems, Dynamical System, Feedback, Feedback Control System, Gain Scheduling, Linear system, Machine Learning, Model Predictive Control, Nonlinear System, Observer, Signal, Sliding Mode Control, System identification, Variable Structure Control.

Algorithms denote computation with iteration. If the algorithms admit only static data, or there is no feedback involved, then the computation can be said to be static. If the algorithm feeds its output to a dynamical system while it receives its input from the same system, the computation is dynamic.

Automation: the process of imbuing or augmenting a system with self directed behaviour that it would otherwise not have.

Controller: A part of an system that has an input-output relationship that serves, or could be used, to make the system behave desirably. Desirable performance can be encoded as a cost function that is dynamically minimised by the controller, thus functioning as a dynamic optimisation engine.

A controller is implemented to effect a constrained change in a dynamical system.

Control engineering is the development of a system that dynamically optimises static or dynamic objective functions given a dynamic system that describes the constraints.

Control System: An identifiable collection of interacting parts which has interactions within it that operate so as to ensure that the overall collection retains its integrity or a desired behaviour.

A control system is a system that has a deliberately integrated mechanism (the controller) that modifies its behaviour according to a desired (or desirable) performance objective.

Cyber-physical systems are systems that have an element that admits automation and communication functions in such a way as to be regarded as part of the behaviour of the system.

Dynamical system: A system that has internal patterns that determine the rate of state changes. Modelling a dynamical system is the attempt to identify states and their associated patterns of change in time that sufficiently identify the output behaviour of the system given an input signal.

Feedback: To feed the actual, measured, or estimated behaviour markers of a system to the decision making organ of a control system. This organ, the controller, uses this information to decide what signal to give to the controlled system such that a desired behaviour of the system is achieved.

A feedback control system couples a controller and a controlled system (the process/plant) using some feedback (or kickback) arrangement. The feedback specified in terms of the systems past, current, or estimated future behaviour.

Gain scheduling says what it means: schedule the controller gain to vary in order to minimise system operational costs or according to system operating region. It is like variable ‘variable structure control’ that does not use a (single) sliding mode. And where the costs are from future projections, we have something like ‘model predictive control.’

Linear system: Every term in a linear system consists of a single state variable or its derivative, scaling a coefficient that is not a function of any state.

Machine Learning: Learning the model, patterns, or characteristics of a machine using a static learning algorithm that uses the machines output as its input. (If the algorithm was a dynamical system, then we may speak of ‘observers.’)

Machine Learning takes static or dynamic data from the output of a system, feeds it to a process that involves the use of static algorithm in order to put out patterns, or models, that may be used to understand/identify the current behaviour/characteristics, and/or the future aspirations of the system.

Model Predictive Control (MPC) is a model of human decision making:
finding the series of input per time (the plan, control signal computation)
that ‘best’ satisfy an objective (the goal, performance index, cost function, objective function)
over a horizon (say, the near future, length of behaviour prediction),
subject to known constraints (internal and external environment, input and output constraints),
and using an uncertain model (chance and reality happening) of how the body (system, life, or world) actually responds.

It tests some series of inputs on a model to see the output it yields over several steps; then it applies the first (series of) input(s) from the series of inputs tested that gave the best results. And it repeats this as a cycle so that the final objective is achieved. Thus, while the objective may stay the same, the plan may be changed because of uncertainties, and chance showing up.

MPC is like an early implementation of machine learning; which, rather than learning a model or pattern, learns a control signal appropriate to an objective.

A nonlinear system is a linear system that has, as it were, state variable variables. It is a system whose model has any term with any combination of state variables and/or state derivatives.

state variables terms with fixed signs, or have terms that include products of state variables of any power (not zero certainly).

Observer: A dynamical system used to estimate the internal states of a system. Its typical inputs are the input signal to the system to be ‘observed,’ and a function of both the output signal of that system and its own output.

Signal: that which has size and sign; the representation of a trajectory. It performs the function of stimulus or response.

Sliding mode control: A control design method that involves determining a function that encodes a stable dynamic system that partitions the state space of the subject system into two; this, such that a control signal is determined from the sign of the partitioning function with the objective to maintain the behaviour at the interface of the two partitions.

System Identification: Modelling a dynamical system using input and output data.

Variable structure control: A control system whose controller changes the characteristic behaviour (or structure) of the overall system based on its location in the state space.