A
proportional control system is a type of linear
feedbackFeedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
control systemA control system is a device or set of devices to manage, command, direct or regulate the behavior of other devices or systems.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...
. Two classic mechanical examples are the toilet bowl float proportioning valve and the
fly-ball governorA centrifugal governor is a specific type of governor that controls the speed of an engine by regulating the amount of fuel admitted, so as to maintain a near constant speed whatever the load or fuel supply conditions...
.
The proportional control system is more complex than an on-off control system like a
thermostatA thermostat is a device for regulating the temperature of a system so that the system's temperature is maintained near a desired setpoint temperature. The name is derived from the Greek words thermos "hot" and statos "a standing"...
, but simpler than a
proportional-integral-derivativeA proportional–integral–derivative controller is a generic control loop feedback mechanism widely used in industrial control systems...
(PID) control system used in something like an automobile
cruise controlCruise control is a system that automatically controls the speed of a motor vehicle. The system takes over the throttle of the car to maintain a steady speed as set by the driver.-History:...
.
An on-off control is like driving a car by applying either full power or no power and varying the
duty cycleIn telecommunications and electronics, the duty cycle is the fraction of time that a system is in an "active" state. In particular, it is used in the following contexts:...
, to control speed.
A
proportional control system is a type of linear
feedbackFeedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
control systemA control system is a device or set of devices to manage, command, direct or regulate the behavior of other devices or systems.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...
. Two classic mechanical examples are the toilet bowl float proportioning valve and the
fly-ball governorA centrifugal governor is a specific type of governor that controls the speed of an engine by regulating the amount of fuel admitted, so as to maintain a near constant speed whatever the load or fuel supply conditions...
.
The proportional control system is more complex than an on-off control system like a
thermostatA thermostat is a device for regulating the temperature of a system so that the system's temperature is maintained near a desired setpoint temperature. The name is derived from the Greek words thermos "hot" and statos "a standing"...
, but simpler than a
proportional-integral-derivativeA proportional–integral–derivative controller is a generic control loop feedback mechanism widely used in industrial control systems...
(PID) control system used in something like an automobile
cruise controlCruise control is a system that automatically controls the speed of a motor vehicle. The system takes over the throttle of the car to maintain a steady speed as set by the driver.-History:...
.
An on-off control is like driving a car by applying either full power or no power and varying the
duty cycleIn telecommunications and electronics, the duty cycle is the fraction of time that a system is in an "active" state. In particular, it is used in the following contexts:...
, to control speed. The power would be on until the target speed is reached, and then the power would be removed, so the car reduces speed. When the speed falls below the target, with a certain
hysteresisA system with hysteresis has memory. Such a system is said to exhibit path-dependence, or "rate-independent memory". .In a deterministic system with no dynamics or hysteresis, it is possible to predict the system's output at an instant in time, given only its input at that instant in time...
, full power would again be applied. It can be seen that this looks like
pulse-width modulationPulse-width modulation is a very efficient way of providing intermediate amounts of electrical power between fully on and fully off. A simple power switch with a typical power source provides full power only, when switched on...
, but would result in poor control.
Proportional control is how most drivers control the speed of a car. If the car is at target speed and the speed increases slightly, the power is reduced slightly, or in proportion to the error (the actual versus target speed), so that the car reduces speed gradually and reaches the target point with very little, if any, "overshoot", so the result is much smoother control than on-off control.
Further refinements like PID control would help compensate for additional variables like hills, where the amount of power needed for a given speed change would vary, which would be accounted for by the integral function of the PID control.
Proportional Control Theory
In the proportional control algorithm, the controller output is directly proportional to the error signal, which is the difference between the
set pointSetpoint is the target value that an automatic control system, for example PID controller, will aim to reach. For example, a boiler control system might have a temperature setpoint, that is a temperature the control system aims to attain....
and the
process variableA process variable is the current status of a process under control. An example of this would be the temperature of a furnace. The current temperature is called the process variable, while the desired temperature is known as the setpoint....
. In other words, the output of a proportional controller is the multiplication product of the error signal and the proportional gain.
This can be mathematically expressed as
where
- : Output of the proportional controller
- : Proportional gain
- : Instantaneous process error at time 't'.
- SP: Set point
- PV: Process variable
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