Hybrid Observer and Genetic Algorithm Cut Simulated Induction Motor Speed Tracking Errors

In an engineering study evaluating industrial electric motor drives, researchers developed an integrated control framework combining a hybrid state estimator with multi-objective evolutionary parameter tuning, substantially reducing speed tracking deviations and electromagnetic fluctuations in simulated induction motors. Speed-sensorless induction-motor drives operate without physical shaft-mounted speed sensors, such as mechanical encoders, relying instead on terminal electrical measurements of stator voltages and currents to reconstruct internal states. While the elimination of shaft-end speed sensors lowers hardware expenses, simplifies installation, and eliminates common mechanical failure points, conventional sensorless drives frequently encounter significant flux estimation errors at low operational speeds, suffer from delayed dynamic responses, and demonstrate vulnerability to motor parameter variations. Furthermore, the high-frequency switching characteristic of traditional sliding-mode control schemes typically introduces severe chattering, degrading the overall smoothness of electromagnetic torque output and phase currents.

To overcome these combined estimation and control hurdles, the researchers formulated a hybrid sliding-mode observer-based optimized control architecture, abbreviated as HSMO-OC, designed specifically for speed-sensorless induction-motor systems. At the foundation of this setup is a hybrid sliding-mode observer that dynamically merges mathematical estimates from voltage-model and current-model flux observers. In standard motor operations, voltage-based flux models perform reliably at higher speeds but become severely compromised in low-speed regimes where the motor back electromotive force is inherently weak; conversely, current-based flux models exhibit superior stability at low velocities but drift under shifting operational parameters. The proposed hybrid observer incorporates speed-dependent weighting functions to balance and blend these two underlying models across the entire operating range, applying continuous sliding-mode error feedback and boundary-layer saturation functions to mitigate chattering and enhance observation accuracy.

Rather than designing observer mechanisms and speed controllers in isolation, the study integrated a multi-objective genetic algorithm, or MOGA, to jointly calibrate the sensitive parameters across both the observer and the sliding-mode speed controller. Motor control systems typically involve tightly coupled variables where adjusting a single gain to accelerate transient tracking speed often magnifies high-frequency torque chatter or amplifies current ripple. Acting as an offline optimization platform, the genetic algorithm simultaneously minimized three competing objective metrics: a normalized speed estimation error, a dynamic response index, and an electromagnetic ripple criterion. The algorithm explored the multidimensional parameter domain subject to rigorous Lyapunov stability criteria alongside practical physical thresholds, including peak phase current limits and permissible electromagnetic torque boundaries, successfully identifying a balanced Pareto-optimal parameter set without altering the physical sliding-mode vector control structure.

To evaluate the control architecture, the investigators conducted comprehensive offline numerical simulations within a MATLAB and Simulink R2022b computing environment running on a 64-bit Windows system powered by an Intel Core i7-12700 processor with 16 gigabytes of memory. The simulated electromechanical plant modeled a 2.2-kilowatt, 380-volt, 50-hertz induction motor operating at a rated nominal speed of 1,430 revolutions per minute with two pole pairs. Specified physical parameters for the virtual machine included a stator resistance of 3.67 ohms, a rotor resistance of 2.10 ohms, mutual inductance of 0.217 henries, and stator and rotor inductances of 0.225 henries. The simulated power stage incorporated a direct-current link voltage of 540 volts, an inverter switching frequency of 10 kilohertz, and a control sampling period of 50 microseconds, alongside designated proportional-integral current-loop gains.

The experimental protocol subjected the virtual motor drive to a rigorous multi-stage performance evaluation encompassing startup acceleration, rapid speed transitions, abrupt load disturbances, and low-speed regulation under weak back electromotive force. During the primary speed-tracking trial, the drive accelerated from standstill to 1,000 revolutions per minute at 0.2 seconds, stepped up to 1,400 revolutions per minute at 0.8 seconds, and subsequently decelerated down to 800 revolutions per minute at 1.4 seconds. To scrutinize disturbance rejection, a external load torque of 7.5 newton-meters was suddenly applied at 0.8 seconds and abruptly removed at 1.4 seconds. In addition, low-speed observability was tested under a steady command of 100 revolutions per minute while sustaining a 3.0 newton-meter load torque, directly examining observer stability under diminished signal-to-noise ratios and low voltage generation.

To isolate the precise performance benefits provided by the hybrid observer architecture versus those delivered by the multi-objective parameter optimization algorithm, the research team instituted a rigorous four-way ablation analysis alongside a standard proportional-integral baseline. All compared configurations operated under completely identical machine parameters, inverter configurations, sampling rates, speed profiles, and load cycles. The baseline configuration comprised a conventional sliding-mode observer coupled to a sliding-mode controller, designated SMO-SMC. The second configuration, HSMO-SMC, replaced only the estimator with the new hybrid observer while retaining manual tuning. The third configuration, MOGA-SMO-SMC, applied multi-objective genetic parameter tuning to the conventional observer-controller pair. Finally, the full HSMO-OC scheme combined the hybrid observer architecture with the jointly optimized parameter vector.

Under the dynamic variable-speed test profile, the baseline SMO-SMC configuration exhibited pronounced transient deviations and protracted recovery intervals, registering a full-cycle speed root-mean-square error of 28.9 revolutions per minute and a maximum transient speed error of 72.6 revolutions per minute. Applying the hybrid observer alone in HSMO-SMC lowered the root-mean-square error to 18.7 revolutions per minute and the maximum error to 48.5 revolutions per minute, reflecting respective reductions of 35.3 percent and 33.2 percent. Similarly, implementing MOGA tuning independently in MOGA-SMO-SMC reduced the speed root-mean-square error to 16.4 revolutions per minute and the maximum error to 43.1 revolutions per minute. When unified in the HSMO-OC framework, the system demonstrated superior tracking accuracy, cutting the overall speed root-mean-square error to 9.6 revolutions per minute—a 66.8 percent reduction compared to the baseline—and trimming the peak transient speed error to 24.7 revolutions per minute, representing a 66.0 percent decline.

Dynamic disturbance rejection and transient settling times exhibited comparable substantial enhancements under the optimized hybrid framework. During startup to the 1,000 revolutions per minute target, the baseline SMO-SMC, HSMO-SMC, MOGA-SMO-SMC, and HSMO-OC configurations attained peak speed overshoots of approximately 1,106, 1,073, 1,058, and 1,029 revolutions per minute, corresponding to settling times of 0.204, 0.178, 0.151, and 0.109 seconds, while a conventional proportional-integral controller required 0.312 seconds to settle. Following the sudden application of the 7.5 newton-meter load torque at 0.8 seconds, maximum transient speed drops were recorded at 91.2 revolutions per minute for proportional-integral control, 64.8 for baseline SMO-SMC, 46.9 for HSMO-SMC, 39.6 for MOGA-SMO-SMC, and only 21.5 revolutions per minute for HSMO-OC. Under HSMO-OC, the motor speed dropped briefly to 978.5 revolutions per minute before recovering completely within the two-percent reference tolerance band in less than 0.12 seconds.

In low-speed testing conducted at 100 revolutions per minute under a constant 3.0 newton-meter load torque, the four ablation setups demonstrated steady-state speed root-mean-square errors of 8.9, 5.4, 4.7, and 2.8 revolutions per minute, alongside maximum tracking errors of 23.4, 15.7, 13.8, and 8.6 revolutions per minute, respectively. Crucially, steady-state electromagnetic smoothness showed notable improvements when evaluating the operational window between 0.90 and 1.10 seconds. Comparing the manually tuned HSMO-SMC setup against HSMO-OC revealed that multi-objective parameter tuning alone reduced root-mean-square torque ripple from 0.76 to 0.41 newton-meters, marking a 46.1 percent reduction. Simultaneously, stator current-ripple root-mean-square levels fell from 0.83 amperes down to 0.48 amperes, reflecting a 42.2 percent reduction, confirming that the continuous boundary layer and coordinated controller gains successfully alleviated high-frequency chattering without lengthening transient settling times.

The investigation also tested the stochastic search efficacy of the genetic algorithm against four benchmark multi-objective optimization algorithms: decomposition-based MOEA/D-DE, reference-point-based NSGA-III, multi-objective particle swarm optimization (MOPSO), and multi-objective grey wolf optimization (MOGWO). Each algorithm executed 30 independent runs under an identical evaluation budget of 5,000 function evaluations across a population of 50 individuals over 100 generations. MOGA achieved an average hypervolume metric of 0.846 ± 0.018 and an inverted generational distance of 0.042 ± 0.007, statistically outperforming the competing algorithms as confirmed by Friedman tests and post-hoc Wilcoxon signed-rank tests with Holm correction at significance levels below 0.001. Subsequent robustness simulations subjected HSMO-OC to independent disturbance conditions, including a 20 percent increase in stator and rotor resistances, measurement noise at a 30-decibel signal-to-noise ratio, and a 3-microsecond inverter dead time, yielding speed root-mean-square errors of 13.4, 12.7, and 14.2 revolutions per minute, compared to baseline SMO-SMC errors of 34.8, 32.1, and 36.5 revolutions per minute.

The study authors explicitly noted key limitations governing their findings, emphasizing that all reported data originated strictly from offline MATLAB and Simulink simulations rather than hardware-in-the-loop platforms or physical dynamometer testbenches. Real-world phenomena such as digital processing latencies, analog sensor drift, high-temperature thermal resistance variations, magnetic saturation, and continuous zero-speed field operation were not experimentally verified. Planned future research will involve implementing the observer and controller algorithms on an embedded digital signal processor coupled to a physical 2.2-kilowatt induction motor, using a shaft-mounted optical encoder solely as an independent measurement benchmark to validate whether these simulated speed accuracy, disturbance resilience, and chattering suppression advantages hold in physical industrial deployments.

Subject of Research: Speed-sensorless sliding-mode vector control optimization for induction motors using hybrid observers and genetic algorithms

Article Title: Multi-objective optimization of speed-sensorless sliding mode vector control for electric motors based on HSMO and MOGA

Article References: Liu, Y., & Zuo, J. (2026). Multi-objective optimization of speed-sensorless sliding mode vector control for electric motors based on HSMO and MOGA. Frontiers in Mechanical Engineering, 12, 1938358. https://doi.org/10.3389/fmech.2026.1938358

Image Credits: AI Generated

DOI: 10.3389/fmech.2026.1938358

Keywords: induction motors, speed sensorless control, sliding mode control, hybrid sliding mode observer, multi objective genetic algorithm, vector control, rotor flux estimation, torque ripple reduction, chattering suppression, MATLAB Simulink, Pareto optimization, parameter tuning, robust control, stator current ripple, electromechanical drives, field oriented control, hypervolume metric