PID is a control algorithm that robots use to move precisely to a target position, speed, or orientation. It stands for Proportional, Integral, and Derivative, which are three mathematical terms that work together to continuously correct errors in real time. If a robotic arm needs to rotate exactly 90 degrees, or a drone needs to hold steady at a specific altitude, a PID controller is almost certainly doing the work behind the scenes.
PID is the most widely used feedback controller in robotics and industrial automation. It works by constantly measuring the gap between where a system is and where it should be, then calculating the right amount of corrective force to close that gap smoothly.
How the Feedback Loop Works
A PID controller operates as a closed-loop system. “Closed loop” means the controller doesn’t just send commands blindly. It reads sensor data, compares the actual state of the robot to the desired state, and adjusts its output based on the difference. That difference is called the error.
Here’s the cycle in plain terms: you tell the robot where to be (the reference or setpoint), a sensor measures where it actually is (the output), and the controller calculates how far off it is (the error). The controller then sends a corrective signal to the motor or actuator, the robot moves, the sensor takes a new reading, and the whole loop repeats. In digital systems, this loop runs hundreds or thousands of times per second.
The Three Terms: P, I, and D
Each letter in PID represents a different strategy for reducing error. They handle different aspects of the problem, and combining all three produces smooth, accurate control.
Proportional (P)
The proportional term responds to the current size of the error. If the robot is far from its target, the correction is large. If it’s close, the correction is small. Think of it like a spring pulling you toward a goal: the further away you are, the harder it pulls. The strength of this response is set by a gain value. Increasing that gain makes the system react more aggressively to errors, but pushing it too high causes the system to overshoot the target and oscillate back and forth.
Proportional control alone often can’t eliminate error completely. A small residual gap, called steady-state error, tends to persist because the corrective force shrinks as the robot gets close to the target but never quite reaches zero.
Integral (I)
The integral term tracks the accumulated error over time. If the proportional term leaves a small persistent gap, the integral term notices that the error has been sitting there and gradually increases the corrective signal until the gap disappears. It’s essentially the controller’s memory. Even a tiny error, if it sticks around long enough, will build up enough integral action to push the system the rest of the way to its target.
The tradeoff is that integral action can make a system sluggish or cause it to overshoot if the gain is set too high. There’s also a well-known problem called integral windup: if the robot can’t physically respond fast enough (say, a motor is already at full power), the integral term keeps accumulating error it can’t act on. When conditions change, all that stored-up correction releases at once, causing a large overshoot. Engineers prevent this with techniques like clamping (stopping the accumulation when the output is already maxed out) or back-calculation (resetting the integral when the system detects saturation).
Derivative (D)
The derivative term responds to how fast the error is changing. If the robot is approaching its target quickly, the derivative acts as a brake, reducing the corrective signal before the robot overshoots. If the error suddenly starts growing, the derivative kicks in early, even while the total error is still small. This gives the controller a predictive quality, reacting to trends rather than just the current state.
Derivative control is sensitive to noise in sensor data. Small, rapid fluctuations in readings get amplified because the derivative cares about the rate of change, not the size. A common fix is applying a low-pass filter to smooth out the derivative signal. One approach uses an exponential moving average, which blends each new reading with previous ones to dampen the jitter while still catching real changes in direction.
Where PID Shows Up in Robotics
Almost any robotic system that needs to hold a position, follow a path, or maintain a speed uses some form of PID control. The applications range from simple wheeled robots to complex aerial vehicles.
In mobile robots, magnetic encoders on each wheel measure rotational speed and direction. Hall-effect sensors inside the encoder generate two signals offset by 90 degrees, creating a pattern that tells the controller both how fast the wheel is spinning and which way. By measuring the time between signal edges, the microcontroller calculates instantaneous wheel velocity. A six-pole magnetic encoder can provide 12 velocity updates per rotation of the motor, with effective measurement resolution exceeding 16 bits at full speed. The PID loop compares this measured velocity to the target velocity and adjusts motor power accordingly, dozens of times per second.
Quadcopter drones are one of the more dramatic examples. A drone uses an inertial measurement unit containing three-axis accelerometers and three-axis gyroscopes to track its position, tilt, speed, and rotation rates. The flight controller maintains a 12-dimensional state vector covering position, orientation, velocity, and angular velocity. Multiple PID loops run simultaneously: one set controls roll, pitch, and yaw angles, while outer loops handle altitude and horizontal position. The controller continuously converts the difference between the drone’s actual position and its desired position into motor speed adjustments across all four rotors.
Robotic arms use PID at each joint. Every joint has its own sensor (usually an encoder) and its own PID loop controlling angle or torque. When you see a robot arm smoothly placing a component on an assembly line, each joint is independently running its PID cycle to reach and hold the correct angle without overshooting or vibrating.
Tuning the Gains
A PID controller only works well if its three gain values are set correctly for the specific system. Setting these values is called tuning, and it’s part science, part trial and error.
The most classic method is Ziegler-Nichols tuning. In the closed-loop version, you start by turning off the integral and derivative terms entirely. Then you gradually increase the proportional gain while giving the system small disturbances. At some point, the system will start oscillating with a constant amplitude, neither growing nor shrinking. You record that gain value (called the ultimate gain) and the period of the oscillation. These two numbers plug into a simple table that gives you starting values for all three gains. For a full PID controller, you set the proportional gain to 60% of the ultimate gain, the integral time to half the oscillation period, and the derivative time to one-eighth of the oscillation period.
These formulas give a reasonable starting point, but most real systems need further hand-tuning. Engineers typically adjust proportional gain first to get the system responding at roughly the right speed, then add integral action to eliminate steady-state error, then add derivative action to reduce overshoot. Modern robotics platforms often include software tools that automate or assist with this process.
When PID Isn’t Enough
PID works extremely well for single-input, single-output systems with relatively predictable behavior. It’s simple to implement, runs efficiently on low-cost microcontrollers, and decades of engineering experience make it well understood. For the vast majority of robotic motor control, temperature regulation, and position-holding tasks, PID is the right tool.
It starts to struggle with systems that have hard physical limits or need to coordinate multiple variables simultaneously. A tank that must reach a specific fill level without ever overflowing, for example, puts PID at a disadvantage. In testing at Chalmers University of Technology, a Model Predictive Controller (MPC) reached the target level more than four times faster than a PID controller in one scenario. More importantly, when the target was set close to the tank’s maximum capacity, the PID controller caused the tank to overflow while the MPC kept levels within bounds. MPC achieves this by looking ahead and planning a sequence of future actions rather than reacting only to the current error.
For highly dynamic robots like humanoids or legged machines navigating rough terrain, controllers like LQR (which optimizes across multiple state variables simultaneously) or MPC are often layered on top of or in place of PID loops. But even in these advanced systems, PID frequently handles the low-level motor control underneath. It remains the foundation that more sophisticated strategies build upon.