MIMO intelligent-PID controller design for half car system based on model free control technique
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Summary
This paper presents a novel Multi-Input-Multi-Output (MIMO) intelligent Proportional-Integral-Derivative (i-PID) controller designed for active suspension systems using a half-car model. The research addresses the limitations of traditional control strategies, such as Linear Quadratic Regulator (LQR) and classical PID, which often require precise mathematical models, extensive sensor arrays, and complex tuning processes. The primary motivation is to improve vehicle ride comfort and safety by effectively damping vibrations caused by road excitations while maintaining robustness against parametric uncertainties and nonlinearities. The proposed method leverages Model Free Control (MFC) theory, specifically utilizing an ultra-local model and an algebraic online compensator to estimate and reject disturbances without relying on statistical techniques or detailed system dynamics. The methodology involves applying the i-PID strategy to a four-degree-of-freedom half-car model, which accounts for both vertical body displacement and pitch motion. Unlike conventional approaches that require multiple sensors for state estimation, this design utilizes only two accelerometers placed at the corners of the sprung mass. The controller integrates a non-asymptotic algebraic observer into the PID structure, allowing for the online estimation of perturbations and automatic adjustment of scaling parameters. The study evaluates the controller’s performance through simulations comparing it against passive suspension, classical PID, and LQR controllers. The testing scenarios include time-domain responses to a specific road bump, frequency-domain analysis across a 0–20 Hz range, and robustness tests involving variations in vehicle load, speed, road roughness, and nonlinear spring/damper characteristics. The results demonstrate that the i-PID controller significantly outperforms the other methods in key performance metrics. In time-domain simulations, the i-PID achieved the highest attenuation of vertical acceleration (66%) and angular acceleration (59%) compared to passive systems, surpassing both PID and LQR. It also provided superior suspension deflection control and road holding stability, ensuring tire contact with the road. Frequency-domain analysis confirmed that the i-PID minimized vertical acceleration gains in the critical 4–8 Hz range associated with ride comfort. Furthermore, robustness tests revealed that the i-PID maintained consistent performance despite a 30% increase in vehicle mass and changes in road class and speed, whereas PID and LQR controllers required recalibration or suffered performance degradation. The controller also effectively handled nonlinearities without parameter retuning. The significance of this work lies in offering a robust, computationally efficient, and easily implementable control solution for active suspensions. By eliminating the need for complex model identification and reducing sensor requirements to just two accelerometers, the i-PID controller lowers implementation costs and complexity. Its ability to automatically adapt to changing conditions and reject disturbances online makes it a superior alternative to traditional methods for enhancing ride comfort and vehicle safety. The study concludes that this model-free approach provides a practical compromise between performance and implementation feasibility, with future work directed toward experimental validation.
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | Crossref | — | — | 1 | 2026-06-25 |
| archive | success | canonical_url | — | — | 1 | 2026-06-26 |
| extract | success | cached | — | — | 2 | 2026-06-26 |
| clean | success | clean | — | — | 1 | 2026-06-26 |
| chunk | success | chunk | — | — | 1 | 2026-06-26 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-26 |
| enrich | success | openalex | — | — | 1 | 2026-06-26 |
| promote | success | — | — | — | 1 | 2026-06-25 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 1 | 2026-06-26 |
| tag | success | vector_similarity | — | — | 6 | 2026-06-26 |
| verify | success | — | — | — | 1 | 2026-06-26 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.
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