Adaptive Smith Predictor with Resonance Compensator (ASP-NRC) for Time-Delay Systems with Mechanical Resonance
Keywords:
Adaptive control, Fractional-delay FIR filter Smith predictor, Gain scheduling, Notch filters, Mechatronic systemsAbstract
Time delays and mechanical resonance frequently coexist in industrial servo systems such as robotic manipulators, high-speed servos, and active magnetic bearings AMBs. This paper presents an Adaptive Smith Predictor with Resonance Compensator ASP-NRC that simultaneously addresses both challenges. The architecture integrates: i. a full-gain Smith predictor λs=1 with a correctly implemented causal fractional-delay FIR filter whose bulk delay is explicitly separated; ii. a series adaptive notch filter whose zeros cancel the plant poles and whose pole -factor is adapted via an envelope-based scheduler; and iii. a rigorous modular stability analysis establishing uniform ultimate boundedness UUB of all closed-loop signals. Extensive simulations over six benchmark cases with Monte Carlo trials, colored noise, robustness to resonance-frequency mismatch, and severe simultaneous parameter uncertainties show that ASP-NRC outperforms PID, Smith predictor, and Smith + fixed-notch controllers. For the nominal case, ASP-NRC achieves 98.1% ISE reduction versus PID and maintains >5 dB resonance suppression for frequency mismatches up to ±5. Under ideal parameter matching, suppression reaches SdB=-85.18 dB i.e., 85.18 dB effective suppression at the resonance frequency. The controller remains stable under severe combined uncertainties ±20% on all parameters.
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