Misplaced Pages

Controller (control theory): Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactively← Previous editContent deleted Content addedVisualWikitext
Revision as of 14:45, 30 May 2012 edit69.156.81.170 (talk) Triple-fixed.← Previous edit Latest revision as of 17:54, 4 September 2017 edit undoDougsim (talk | contribs)Extended confirmed users8,815 edits Made into a rediect page, as the topic is fully covered in control theory, and the title actually implies it is a part of control theory, so not need to duplicate here. 
(26 intermediate revisions by 17 users not shown)
Line 1: Line 1:
{{unreferenced|date=January 2009}}
In ], a '''controller''' is a device, possibly in the form of a chip, analogue electronics, or computer, which monitors and physically alters the operating conditions of a given ].<ref name="The Principal Goal of Control">{{cite book|last=Salgado|first=Graham C. Goodwin, Stefan F. Graebe, Mario E.|title=Control System Design|year=2001|publisher=Prentice Hall|location=Upper Saddle River, N. J.|isbn=0139586539}}</ref>{{rp|p.21}}


== Input and Control Variables == #REDIRECT ]

Depending on the set-up of the physical or non-physical system certain operating conditions are referred to as controlled output variables which can be affected by adjusting certain input variables. Upon receiving the input signal the controller attempts to regulate controlled output behaviour, either by attenuating or amplifying the output signal to achieve a desired result.

For example, the heating system of a house can be equipped with a thermostat (controller) for sensing air temperature (output variable) which can turn on or off a furnace or heater when the air temperature drops or exceeds a desired temperature, otherwise known as the setpoint.

In this example, the thermostat is the controller, receiving information of its surroundings which it then uses to regulate the activity of the heater. The heater is the processor that warms the air inside the house to the desired setpoint, usually room temperature. A number of other examples are given in the table below. <ref name="The Principal Goal of Control"/>{{rp|p.19}}

{| class="wikitable"
|-
! System !! Controlled Outputs Include !! Controller !! Desired Performance Includes
|-
| Aircraft || Course, pitch, roll, yaw || Autopilot || Maintain flight path on a safe and smooth trajectory
|-
| Furnace || Temperature || Temperature controller || Follow warm-up temperature profile, then maintain temperature
|-
| Waster treatment || pH value of effluent || pH controller || Neutralize effluent to specified accuracy
|-
| Automobile || Speed || Cruise Controller || Attain, then maintain selected speed without undue fuel consumption
|}

The notion of controllers can be extended to more complex systems. In the natural world, individual organisms also appear to be equipped with controllers that assure the ] necessary for survival of each individual. Both human-made and natural systems exhibit collective behaviors amongst individuals in which the controllers seek some form of equilibrium

== Types of Controlling System==

In ] there are two basic types of control. These are ] and ]. The input to a feedback controller is the same as what it is trying to control - the controlled variable is "fed back" into the controller. The thermostat of a house is an example of a feedback controller. This controller relies on measuring the controlled variable, in this case the temperature of the house, and then adjusting the output, whether or not the heater is on. However, feedback control usually results in intermediate periods where the controlled variable is not at the desired set-point. With the thermostat example, if the door of the house were opened on a cold day, the house would cool down. After it fell below the desired temperature (set-point), the heater would kick on, but there would be a period when the house was colder than desired.

Feed-forward control can avoid the slowness of feedback control. With feed-forward control, the disturbances are measured and accounted for before they have time to affect the system. In the house example, a feed-forward system may measure the fact that the door is opened and automatically turn on the heater before the house can get too cold. The difficulty with feed-forward control is that the effect of the disturbances on the system must be accurately predicted, and there must not be any unmeasured disturbances. For instance, if a window were opened that was not being measured, the feed-forward-controlled thermostat might still let the house cool down.

To achieve the benefits of feedback control (controlling unknown disturbances and not having to know exactly how a system will respond to disturbances) ''and'' the benefits of feed-forward control (responding to disturbances before they can affect the system), there are combinations of feedback and feed-forward that can be used.

Some examples of where feedback and feed-forward control can be used together are dead-time compensation, and inverse response compensation. '''Dead-time compensation''' is used to control devices that take a long time to show any change to a change in input, for example, change in composition of flow through a long pipe. A dead-time compensation control uses an element (also called a ]) to predict how changes made now by the controller will affect the controlled variable in the future. The controlled variable is also measured and used in feedback control. '''Inverse response compensation''' involves controlling systems where a change at first affects the measured variable one way but later affects it in the opposite way. An example would be eating candy. At first it will give you lots of energy, but later you will be very tired. As can be imagined, it is difficult to control this system with feedback alone, therefore a predictive feed-forward element is necessary to predict the reverse effect that a change will have in the future.
''''''''

== Types of controllers ==

Most control valve systems in the past were implemented using mechanical systems or solid state electronics. Pneumatics were often utilized to transmit information and control using pressure. However, most modern ]s now rely on computers for the '''industrial controller'''. Obviously it is much easier to implement complex control algorithms on a computer than using a mechanical system.

For feedback controllers there are a few simple types. The most simple is like the thermostat that just turns the heat on if the temperature falls below a certain value and off it exceeds a certain value (]).

Another simple type of controller is a ]. With this type of controller, the controller output (control action) is proportional to the error in the measured variable.


In feedback control, it is standard to define the error as the difference between the desired value (setpoint) <math>y_s</math>and the current value (measured) <math>y</math>. If the error is large, then the control action is large. Mathematically:

:<math>u(t) = K_c*e(t)+ u_0</math>

where
:<math>u(t)</math> represents the control action (controller output),
:<math>e(t)=y_s(t)-y(t)</math> represents the error,
:<math>K_c</math> represents the controller's gain, and
:<math>u_o</math> represents the steady state control action (bias) necessary to maintain the variable at the steady state when there is no error.

It is important that the control action <math>u</math> counteracts the change in the controlled variable <math>y</math> (negative feedback). There are then two cases depending on the sign of the process gain.

In the first case the process gain is positive, so an increase in the controlled variable (measurement) <math>y</math> requires a decrease in the control action <math>u</math> (reverse-acting control). In this case the controller gain <math>K_c</math> is positive, because the standard definition of the error already contains a negative sign for <math>y</math>.

In the second case the process gain is negative, so an increase in the controlled variable (measurement) <math>y</math> requires an increase in the control action <math>u</math> (direct-acting control). In this case the controller gain <math>K_c</math> is negative.

A typical example of a reverse-acting system is control of temperature (<math>y</math>) by use of steam (<math>u</math>). In this case the process gain is positive, so if the temperature increases, the steam flow must be decreased to maintain the desired temperature. Conversely, a typical example of a direct-acting system is control of temperature using cooling water. In this case the process gain is negative, so if the temperature increases, the cooling water flow must be increased to maintain the desired temperature.

Although proportional control is simple to understand, it has drawbacks. The largest problem is that for most systems it will never entirely remove error. This is because when error is 0 the controller only provides the steady state control action so the system will settle back to the original steady state (which is probably not the new set point that we want the system to be at). To get the system to operate near the new steady state, the controller gain, Kc, must be very large so the controller will produce the required output when only a very small error is present. Having large gains can lead to system instability or can require physical impossibilities like infinitely large valves.

Alternates to proportional control are proportional-integral (PI) control and ]. PID control is commonly used to implement closed-loop control.

] can be used in systems sufficiently well-characterized as to predict what outputs will necessarily achieve the desired states. For example, the rotational velocity of an ] may be well enough characterized for the supplied ] to make feedback unnecessary.

The drawback of ] is that it requires perfect knowledge of the system (i.e. one knows exactly what inputs to give in order to get the desired output), and it assumes there are no disturbances to the system.

== See also ==
* ]
* ]
* ]
* ]
* ]
* ]
* ]

==References==
{{reflist}}

]
]
]

]
]
]
]
]
]
]
]
]
]
]
]
]
]
]

Latest revision as of 17:54, 4 September 2017

Redirect to: