Discrete Sliding-mode Velocity Estimation And Filter-independent Pid Tuning For Gimbal Bldc Drives

Abstract

Velocity Loops On Low-cost Brushless Drives Are Al-most Always Closed On A Filtered Finite Difference Of A Magnetic Encoder Angle, And Are Almost Always Tuned By Watching That Same Filtered Signal. This Paper Reports A Hardware Study In Which The Practice Is Examined From Both Ends. Four Velocity Estimators — An Unfiltered Finite Difference, A First-order Low-pass Filter, A Two-state Extended Kalman Filter And A Two-state Sliding-mode Observer — Are Evaluated On One 7 Pole-pair Gim-bal Motor Driven By Field-oriented Control On An STM32G431 Microcontroller, All Four Consuming The Same Encoder Sample At The Same Instant. A Discrete Limit Cycle In The Sliding-mode Observer Is First Diagnosed And Removed: The Switching Action Had Been Applied As A Per-sample Increment Rather Than As A Rate Integrated Over The Sample Interval, Which Placed The In-layer Loop Gain Above The Discrete Stability Bound And Produced A 244 RPM Oscillation With The Rotor Held Stationary. With The Update Law Corrected, The Observer Becomes The Least Noisy Of The Four Estimators At Every Speed Tested, With 2.3–5.2 Less Noise Than The Raw Difference And 1.4–1.9 Less Thanthe Kalman Filter. The Corrected Estimator Is Then Used As An Independent Yardstick For A Replicated Velocity-PID Study Of 9 Gain Configurations Over 27 Runs. Scored On The Controller’s Own Feedback Signal, Raising The Feedback Filter Constant From 10 Ms To 50 Ms Appears To Cut Speed Ripple By 14 ; Scored On The Shaft It Cuts It By 1.8 . At A Proportional Gain Of 1.0 The Feedback Signal Reports A Standard Deviation Of 63 RPM While The Shaft Is Steady At 4.8 RPM And Simply Sits 26 RPM Below Setpoint. We Conclude That Such Drives Must Be Tuned Against An Estimate That Does Not Share The Control Filter, And Give A Procedure That Does So.

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