PID controller
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A proportional–integral–derivative controller (PID controller) is a generic .control loop feedback mechanism widely ud in industrial control systems.
A PID controller attempts to correct the error between a measured process variable and a desired tpoint by calculating and then outputting a corrective action that can adjust the process accordingly.
morning dewThe PID controller calculation (algorithm) involves three parate parameters; the Proportional, the Integral and Derivative values. The Proportional value determines the reaction to the current error, the Integral determines the reaction bad on the sum of recent errors and the Derivative determines the reaction to the rate at which the error has been changing. The weightedsum of the three actions is ud to adjust the process via a control element such as the position of a control valve or the power supply of a heating element.By "tuning" the three constants in the PID controller algorithm the PID can provide control action designed for specific process requirements. The respon of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the tpoint and the degree of system oscillation. Note that the u of the PID alg
orithm for control does not guarantee optimal control of the system or system stability.
Some applications may require using only one or two modes to provide the appropriate system control. This is achieved by tting the gain of undesired control outputs to zero. A PID controller will be called a PI, PD, P or I controller in the abnce of the respective control actions. PI controllers are particularly common, since derivative action is very nsitive to measurement noi, and the abnce of an integral value may prevent the system from reaching its target value due to the control action.
A block diagram of a PID controller
Note: Due to the diversity of the field of control theory and application, many naming conventions for the relevant variables are in common u.
1.Control loop basics
A familiar example of a control loop is the action taken to keep one's shower water at the ideal temperature, which typically involves the mixing of two process streams, cold and hot water. The person feels the water to estimate its temperature. Bad on this measurement they perform a contr
diagramol action: u the cold water tap to adjust the process. The person would repeat this input-output control loop, adjusting the hot water flow until the process temperature stabilized at the desired value.
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Feeling the water temperature is taking a measurement of the process value or process variable (PV). The desired temperature is called the tpoint (SP). The output from the controller and input to the process (the tap position) is called the manipulated variable (MV). The difference between the measurement and the tpoint is the error (e), too hot or too cold and by how much.As a controller, one decides roughly how much to change the tap position (MV) after one determines the temperature (PV), and therefore the error. This first estimate is the equivalent of the proportional action of a PID controller. The integral action of a PID controller can be thought of as gradually adjusting the temperature when it is almost right. Derivative action can be thought of as noticing the water temperature is getting hotter or colder, and how fast, and taking that into account when deciding how to adjust the tap.Making a change that is too large when the error is small is equivalent to a high gain controller and will lead to
overshoot. If the controller were to repeatedly make changes that were too large and repeatedly overshoot the target, this control loop would be termed unstable and the output would oscillate aroun
d the tpoint in either a constant, growing, or decaying sinusoid. A human would not do this becau we are adaptive controllers, learning from the process history, but PID controllers do not have the ability to learn and must be t up correctly. Selecting the correct gains for effective control is known as tuning the controller.
If a controller starts from a stable state at zero error (PV = SP), then further changes by the controller will be in respon to changes in other measured or unmeasured inputs to the process that impact on the process, and hence on the PV. Variables that impact on the process other than the MV are known as disturbances and generally controllers are ud to reject disturbances and/or implement tpoint changes. Changes in feed water temperature constitute a disturbance to the shower process.
In theory, a controller can be ud to control any process which has a measurable output (PV), a known ideal value for that output (SP) and an input to the process (MV) that will affect the relevant PV. Controllers are ud in industry to regulate temperature, pressure, flow rate, chemical composition, speed and practically every other variable for which a measurement exists. Automobile crui control is an example of a process which utilizes automated control.
Due to their long history, simplicity, well grounded theory and simple tup and maintenance requirements, PID controllers are the controllers of choice for many of the applications.
2.PID controller theory
Note: This ction describes the ideal parallel or non-interacting form of the PID controller. For other forms plea e the Section "Alternative notation and PID forms".
The PID control scheme is named after its three correcting terms, who sum constitutes the manipulated variable (MV). Hence:
where Pout, Iout, and Dout are the contributions to the output from the PID controller from each of the three terms, as defined below.
2.1. Proportional term
The proportional term makes a change to the output that is proportional to the current error value. The proportional respon can be adjusted by multiplying the error by a constant Kp, called the proportional gain.vine
heatThe proportional term is given by:
Where
Pout: Proportional output毕业设计英文
Kp: Proportional Gain, a tuning parameter
e: Error = SP − PV
t: Time or instantaneous time (the prent)
Change of respon for varying KpA high proportional gain results in a large change in the output for a given change in the error. If the proportional gain is too high, the system can become unstable (See the ction on Loop Tuning). In contrast, a small gain results in a small output respon to a large input error, and a less responsive (or nsitive) controller. If the proportional gain is too low, the control action may be too small when responding to system disturbances.
In the abnce of disturbances, pure proportional control will not ttle at its target value, but will retain a steady state error that is a function of the proportional gain and the process gain. Despite the steady-state offt, both tuning theory and industrial practice indicate that it is the proportional term that should contribute the bulk of the output change.幼儿英语培训
2.2.Integral term
The contribution from the integral term is proportional to both the magnitude of the error and the duration of the error. Summing the instantaneous error over time (integrating the error) gives the accumulated offt that should have been corrected previously. The accumulated error is then multiplied by the integral gain and added to the controller output. The magnitude of the contribution of the integral term to the overall control action is determined by the integral gain, Ki.
The integral term is given by:
Change of respon for varying KiWheredayspring
Iout: Integral output
Ki: Integral Gain, a tuning parameter
lighter fuele: Error = SP − PV
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τ: Time in the past contributing to the integral respon
The integral term (when added to the proportional term) accelerates the
