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PID controller

nounAlso: PID control, proportional–integral–derivative controller, PI controller, three-term controller, PID loop

In plain wordsThe most common automatic controller in industry. It corrects a machine using three ingredients: how far off it is now, how long it has been off, and how fast the error is changing.

  1. A feedback controller that computes its output from the error e(t) between a desired setpoint and a measured value as the sum of three terms: a proportional term, which reacts in proportion to the present error; an integral term, which accumulates past error to remove steady offsets; and a derivative term, which reacts to the error's rate of change to anticipate and damp oscillation. The three gains are tuned by hand, by rules such as the Ziegler–Nichols method, or automatically. Practical implementations guard against integral windup (the integral growing while the actuator is saturated) and derivative kick (spikes when the setpoint jumps), and filter the derivative against sensor noise. PID controllers need no model of the process and work well on many roughly linear systems; they regulate most industrial process loops as well as motor joints, drone attitude, cruise control and thermostats. In robots, PID loops usually run at the lowest level, tracking joint positions or velocities commanded by planners or learned policiespolicy, n.: An AI agent's strategy: the rule it follows to pick an action in each situation. Training in reinforcement learning means improving this rule until it earns high rewards..

    The arm oscillates at the end of each move; lower the proportional gain and add a little derivative.

u(t)=Kp e(t)+Ki∫0te(τ) dτ+Kdde(t)dtu(t) = K_p\, e(t) + K_i \int_0^t e(\tau)\, d\tau + K_d \frac{de(t)}{dt}

Origin

Elmer Sperry built PID-like ship autopilots around 1911. Nicolas Minorsky gave the first theoretical analysis in 'Directional Stability of Automatically Steered Bodies' (Journal of the American Society of Naval Engineers, 1922), modeling how helmsmen respond to present error, accumulated error and rate of change. John Ziegler and Nathaniel Nichols published their tuning rules in 1942.

Usage note

Industrial surveys commonly report that more than nine in ten regulatory control loops are PID or PI, which makes PID the default baseline against which learned controllers are judged.

Related

See also
  • control theorycontrol theory, n.: The mathematics of making machines behave as intended by constantly measuring what they are doing and correcting them, as a thermostat, cruise control or self-balancing robot does.
  • model predictive controlmodel predictive control, n.: A control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements.
  • actuatoractuator, n.: The 'muscle' of a machine: a motor or similar device that turns electrical, hydraulic or air power into movement, such as turning a robot's joint or closing its gripper.
  • optimal controloptimal control, n.: Finding the best way to steer a system over time, such as the most fuel-efficient path for a rocket or the smoothest motion for a robot arm, by minimizing a cost while obeying the laws of motion.
  • impedance controlimpedance control, n.: A way of controlling a robot so that it behaves like a spring and shock absorber when it touches things, giving way gently instead of pushing rigidly.
Contrast with
  • model predictive controlmodel predictive control, n.: A control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements.

Sources

  1. Minorsky, N. (1922). Directional stability of automatically steered bodies. Journal of the American Society of Naval Engineers 34(2), 280–309.
  2. Åström, K. J. & Hägglund, T. (2006). Advanced PID Control. ISA.

Mentioned in

actuatoractuator, n.: The 'muscle' of a machine: a motor or similar device that turns electrical, hydraulic or air power into movement, such as turning a robot's joint or closing its gripper., control theorycontrol theory, n.: The mathematics of making machines behave as intended by constantly measuring what they are doing and correcting them, as a thermostat, cruise control or self-balancing robot does., model predictive controlmodel predictive control, n.: A control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements., impedance controlimpedance control, n.: A way of controlling a robot so that it behaves like a spring and shock absorber when it touches things, giving way gently instead of pushing rigidly.