Comparing LQR, SMC, and Backstepping for Active Suspension: Robustness, Energy Efficiency, and Frequency Response - Ali Aniss Ebrahim (Control Systems and Optimization Letters, 2026)
While active suspension systems have advanced significantly, the literature still lacks a systematic compara tive framework that integrates time-domain robustness analysis, frequency-domain vibration isolation, and operational constraints such as actuator saturation. This study presents a comparative framework to bridge this gap through a quantitative evaluation of three advanced control strategies: Linear Quadratic Regulator (LQR), Sliding Mode Control (SMC), and Backstepping. The strategies were evaluated under multiple test scenarios, including: a step signal (0.05 m for 0.2 s), a 0.02 m amplitude sine wave with varying frequencies between 0.5 and 10 Hz, a random wave, ±20% variations in system parameters, and simulated actuator saturation constraints at ±1500 N. The SMC controller demonstrated exceptional robustness under uncertainty, achieving a 34.2% improvement in suspension deflection, while the LQR controller demonstrated superior energy efficiency, outperforming SMC by 28.5%. Frequency response analysis revealed that LQR is optimal in the low frequency band (0–2 Hz), while SMC excels in the mid band (2–8 Hz). Analysis of variance (ANOVA) confirmed statistically significant differences between the strategies (F(2,87) = 24.36, p 0.001). This framework provides a quantitative trade-off model that guides designers to: use SMC for applications requiring high robustness under uncertain conditions (such as vehicles operating on varying terrain), use LQR when energy efficiency is a top priority (such as electric vehicles), and use Backstepping as a compromise that ensures guaranteed mathematical stability with balanced performance.