Setpoint (control system)

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Block diagram of a negative feedback system used to maintain a setpoint in the face of a disturbance using error-controlled regulation. Positive error means feedback is too small (controller calls for an increase), and negative error means feedback is too large (controller calls for a decrease). Set-point control.png
Block diagram of a negative feedback system used to maintain a setpoint in the face of a disturbance using error-controlled regulation. Positive error means feedback is too small (controller calls for an increase), and negative error means feedback is too large (controller calls for a decrease).

In cybernetics and control theory, a setpoint (SP; [1] also set point) is the desired or target value for an essential variable, or process value (PV) of a control system, [2] which may differ from the actual measured value of the variable. Departure of such a variable from its setpoint is one basis for error-controlled regulation using negative feedback for automatic control. [3] A setpoint can be any physical quantity or parameter that a control system seeks to regulate, such as temperature, pressure, flow rate, position, speed, or any other measurable attribute.

Contents

In the context of PID controller, the setpoint represents the reference or goal for the controlled process variable. It serves as the benchmark against which the actual process variable (PV) is continuously compared. The PID controller calculates an error signal by taking the difference between the setpoint and the current value of the process variable. Mathematically, this error is expressed as:

where is the error at a given time , is the setpoint, is the process variable at time .

The PID controller uses this error signal to determine how to adjust the control output to bring the process variable as close as possible to the setpoint while maintaining stability and minimizing overshoot.

Examples

Cruise control

The error can be used to return a system to its norm. An everyday example is the cruise control on a road vehicle; where external influences such as gradients cause speed changes (PV), and the driver also alters the desired set speed (SP). The automatic control algorithm restores the actual speed to the desired speed in the optimum way, without delay or overshoot, by altering the power output of the vehicle's engine. In this way the error is used to control the PV so that it equals the SP. A widespread of error is classically used in the PID controller.

Industrial applications

Special consideration must be given for engineering applications. In industrial systems, physical or process restraints may limit the determined set point. For example, a reactor which operates more efficiently at higher temperatures may be rated to withstand 500°C. However, for safety reasons, the set point for the reactor temperature control loop would be well below this limit, even if this means the reactor is running less efficiently.

See also

Related Research Articles

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Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.

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<span class="mw-page-title-main">Negative feedback</span> Reuse of output to stabilize a system

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<span class="mw-page-title-main">Thermostat</span> Component which maintains a setpoint temperature

A thermostat is a regulating device component which senses the temperature of a physical system and performs actions so that the system's temperature is maintained near a desired setpoint.

<span class="mw-page-title-main">Control system</span> System that manages the behavior of other systems

A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process.

<span class="mw-page-title-main">Closed-loop controller</span> Feedback controller

A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs have an effect on the process outputs, which is measured with sensors and processed by the controller; the result is "fed back" as input to the process, closing the loop.

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Integral windup, also known as integrator windup or reset windup, refers to the situation in a PID controller where a large change in setpoint occurs and the integral term accumulates a significant error during the rise (windup), thus overshooting and continuing to increase as this accumulated error is unwound. The specific problem is the excess overshooting.

<span class="mw-page-title-main">Bang–bang control</span> Binary feedback controller

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The Ziegler–Nichols tuning method is a heuristic method of tuning a PID controller. It was developed by John G. Ziegler and Nathaniel B. Nichols. It is performed by setting the I (integral) and D (derivative) gains to zero. The "P" (proportional) gain, is then increased until it reaches the ultimate gain, at which the output of the control loop has stable and consistent oscillations. and the oscillation period are then used to set the P, I, and D gains depending on the type of controller used and behaviour desired:

Classical control theory is a branch of control theory that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback, using the Laplace transform as a basic tool to model such systems.

Linear control are control systems and control theory based on negative feedback for producing a control signal to maintain the controlled process variable (PV) at the desired setpoint (SP). There are several types of linear control systems with different capabilities.

References

  1. B. Wayne Bequette (2003). Process Control: Modeling, Design, and Simulation. Prentice Hall Professional. p. 5. ISBN   9780133536409.
  2. An 'essential variable' is defined as "a variable that has to be kept within assigned limits to achieve a particular goal": Jan Achterbergh, Dirk Vriens (2010). "§2.3 Cybernetics: Effective methods for the control of complex systems". Organizations: Social Systems Conducting Experiment. Springer Science & Business Media. p. 47. ISBN   9783642143168.
  3. W. Ross Ashby (1957). "Chapter 12: The error-controlled regulator". Introduction to cybernetics (PDF). Chapman & Hall Ltd.; Internet (1999). pp. 219–243.