When tuning an altitude PID controller for a quadrotor in Simulink, the automated PID Tuner linearizes the model around an operating point and drops the constant gravity term (g), treating it as zero. This causes massive overshoots because the controller does not account for the continuous downward load. The permanent fix is adding a gravity compensation feedforward term (F_ff = m * g) directly to the PID output, leaving the feedback loop to regulate only dynamic deviations.
1. The Core Problem: Why the Simulink PID Tuner Causes Overshoot
When designing an altitude hold loop for a quadrotor or vertical hoist, the one-dimensional vertical motion equation is:
z_ddot(t) = (F_lift(t) / m) - g
Where z is altitude, F_lift is total thrust from the PID controller, m is vehicle mass, and g is gravitational acceleration (9.81 m/s²).
Why Linearization Misses Gravity
The Simulink PID Tuner computes a linear state-space approximation around a specific operating point. During linearization, the constant affine term -g disappears in the derivative, leaving a double-integrator plant: P(s) = 1 / (m * s²).
The tuner designs gains assuming zero steady-state downward force. When executed in the full non-linear model, gravity acts as a massive constant input disturbance. The integrator must accumulate substantial error before generating sufficient counter-thrust, creating severe transient overshoot.
2. Two Ways to Solve the Altitude Disturbance
Method A: Gravity Feedforward Compensation (Recommended)
Because gravity is a known physical constant, calculate the base hover force F_hover = m * g and inject it directly via a Sum block at the PID Controller output. The feedback PID now only calculates dynamic correction thrust (ΔF), ensuring fast settling with 0% overshoot.
Method B: High-Bandwidth Disturbance Rejection (Not Recommended)
Attempting to reject gravity by cranking up the integrator gain (Ki) forces high closed-loop bandwidths that amplify sensor noise, saturate actuators, and introduce phase lag into attitude dynamics.
3. Step-by-Step Single-Loop PID Tuner Workflow
- Insert Controller: Place the standard PID Controller block from the Continuous library into your feedback path.
- Launch Tuner: Open the block dialog and click Tune to automatically linearize the plant model.
- Adjust Sliders: Tune the Response Time (bandwidth) and Transient Behavior (aim for a 60°–70° phase margin).
- Export Gains: Click Update Block to write the tuned Kp, Ki, Kd, and filter divisor N parameters into Simulink.
4. SISO vs. Coupled MIMO Systems
A full 6-DOF quadrotor with 4 rotor inputs controlling 6 degrees of freedom is a coupled MIMO system. For multi-variable control beyond decoupled SISO loops, use:
- Robust Control Toolbox (
systune): Tunes multiple decentralized PID loops simultaneously with robust stability margins. - Simulink Design Optimization: Tunes controllers against non-linear physical constraints such as motor current limits and RPM saturation.
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