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A variable in an experiment which is held constant in order to assess the relationship between multiple variables [a], is a control variable. [2] [3] A control variable is an element that is not changed throughout an experiment because its unchanging state allows better understanding of the relationship between the other variables being tested. [4]
In this case, the control variables may be wind speed, direction and precipitation. If the experiment were conducted when it was sunny with no wind, but the weather changed, one would want to postpone the completion of the experiment until the control variables (the wind and precipitation level) were the same as when the experiment began.
The control action is the switching on/off of the boiler, but the controlled variable should be the building temperature, but is not because this is open-loop control of the boiler, which does not give closed-loop control of the temperature. In closed loop control, the control action from the controller is dependent on the process output.
A variable may be thought to alter the dependent or independent variables, but may not actually be the focus of the experiment. So that the variable will be kept constant or monitored to try to minimize its effect on the experiment. Such variables may be designated as either a "controlled variable", "control variable", or "fixed variable".
A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable (i.e. confounding variables). [1] This increases the reliability of the results, often through a comparison between control measurements and the other measurements.
An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost function. The optimal control can be derived using Pontryagin's maximum principle (a necessary condition also known as Pontryagin's minimum principle or simply Pontryagin's principle), [ 8 ] or by solving the Hamilton ...
A system is said to be stabilizable when all uncontrollable state variables can be made to have stable dynamics. Thus, even though some of the state variables cannot be controlled (as determined by the controllability test above) all the state variables will still remain bounded during the system's behavior. [8]
The Hamiltonian of control theory describes not the dynamics of a system but conditions for extremizing some scalar function thereof (the Lagrangian) with respect to a control variable . As normally defined, it is a function of 4 variables