Control theory: Difference between revisions

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* [[Multiple-input multiple-output system|Multiple-input multiple-output]] (MIMO) – These are found in more complicated systems. For example, modern large [[telescope]]s such as the [[Keck telescopes|Keck]] and [[MMT Observatory|MMT]] have mirrors composed of many separate segments each controlled by an [[actuator]]. The shape of the entire mirror is constantly adjusted by a MIMO [[active optics]] control system using input from multiple sensors at the focal plane, to compensate for changes in the mirror shape due to thermal expansion, contraction, stresses as it is rotated and distortion of the [[wavefront]] due to turbulence in the atmosphere. Complicated systems such as [[nuclear reactor]]s and human [[cell (biology)|cells]] are simulated by a computer as large MIMO control systems.

===Classical SISO Systemsystem Designdesign ===

The scope of classical control theory is limited to [[Single-input single-output system|single-input and single-output]] (SISO) system design, except when analyzing for disturbance rejection using a second input. The system analysis is carried out in the time ___domain using [[differential equations]], in the complex-s ___domain with the [[Laplace transform]], or in the frequency ___domain by transforming from the complex-s ___domain. Many systems may be assumed to have a second order and single variable system response in the time ___domain. A controller designed using classical theory often requires on-site tuning due to incorrect design approximations. Yet, due to the easier physical implementation of classical controller designs as compared to systems designed using modern control theory, these controllers are preferred in most industrial applications. The most common controllers designed using classical control theory are [[PID controller]]s. A less common implementation may include either or both a Lead or Lag filter. The ultimate end goal is to meet requirements typically provided in the time-___domain called the step response, or at times in the frequency ___domain called the open-loop response. The step response characteristics applied in a specification are typically percent overshoot, settling time, etc. The open-loop response characteristics applied in a specification are typically Gain and Phase margin and bandwidth. These characteristics may be evaluated through simulation including a dynamic model of the system under control coupled with the compensation model.

===Modern MIMO Systemsystem Designdesign===

Modern control theory is carried out in the [[stateState space (controls)|state space]], and can deal with [[Multiple-input multiple-output system|multiple-input and multiple-output]] (MIMO) systems. This overcomes the limitations of classical control theory in more sophisticated design problems, such as fighter aircraft control, with the limitation that no frequency ___domain analysis is possible. In modern design, a system is represented to the greatest advantage as a set of decoupled first order [[differential equation]]s defined using [[state variables]]. [[Nonlinear control|Nonlinear]], [[multivariable control|multivariable]], [[adaptive control|adaptive]] and [[robust control]] theories come under this division. Matrix methods are significantly limited for MIMO systems where linear independence cannot be assured in the relationship between inputs and outputs .{{Citation needed|reason=No citation or explanation on this generic claim|date=November 2019}}. Being fairly new, modern control theory has many areas yet to be explored. Scholars like [[Rudolf E. Kálmán]] and [[Aleksandr Lyapunov]] are well known among the people who have shaped modern control theory.

==Topics in control theory==