Najm, M., Younis, A., Majeed, F. (2023). Mathematical Modelling and PID Controller Implementation to Control Linear and Nonlinear Quarter Car Active Suspension. Alustath, 28(2), 113-121. doi: 10.33899/rengj.2023.137327.1216
Mustafa Ibrahim Najm; Alaa Dahham Younis; Firas Ahmed Majeed. "Mathematical Modelling and PID Controller Implementation to Control Linear and Nonlinear Quarter Car Active Suspension". Alustath, 28, 2, 2023, 113-121. doi: 10.33899/rengj.2023.137327.1216
Najm, M., Younis, A., Majeed, F. (2023). 'Mathematical Modelling and PID Controller Implementation to Control Linear and Nonlinear Quarter Car Active Suspension', Alustath, 28(2), pp. 113-121. doi: 10.33899/rengj.2023.137327.1216
Najm, M., Younis, A., Majeed, F. Mathematical Modelling and PID Controller Implementation to Control Linear and Nonlinear Quarter Car Active Suspension. Alustath, 2023; 28(2): 113-121. doi: 10.33899/rengj.2023.137327.1216

Mathematical Modelling and PID Controller Implementation to Control Linear and Nonlinear Quarter Car Active Suspension

Al-Rafidain Engineering Journal (AREJ)
Volume 28, Issue 2, September 2023, Pages 113-121    PDF (721.08 K)
Document Type: Research Paper
DOI: 10.33899/rengj.2023.137327.1216
Authors
Mustafa Ibrahim Najm* 1; Alaa Dahham Younis1; Firas Ahmed Majeed2
1Mechanical Engineering Department, College of Engineering, University of Mosul, Mosul, Iraq
2Mechatronics Engineering Department, College of Engineering, University of Mosul, Mosul, Iraq
Abstract
In this work, linear and nonlinear designs of active suspension models are proposed to develop and improve quarter-car systems. To simplify stability assessment, a second-order system is proposed for both linear and nonlinear cases. The linear system consists of mass, spring, and damper components, while the nonlinear system includes the same components with additional nonlinear parts for stiffness and damper. Moreover, the state space of the linear and nonlinear is presented as a preparatory step before applying the analysis methods to validate the models. After that, the stability of linear and nonlinear systems is characterized using Matlab simulations to compare suspension performance parameters such as rise time (tr), settling time (ts), and peak overshoot (Mp). The simulation results of the linear system for each of tr, ts, Mp were0.097612sec, 2.3 sec, and 0.3839 cm, respectively, while the results of the nonlinear system were 0.52237 sec, 20.16 sec, and 0.3064 cm, respectively. In addition, the results for linear and nonlinear systems indicate the need to improve ride comfort and road handling using PID controller design. Consequently, it is possible to reach a better compromise than is possible using pure elements, without a controller). Finally, the active suspension system for both linear and nonlinear systems is improved through the application of a PID controller, resulting in the following values for the linear system: tr = 0.10721sec, ts = 1.693 sec, and Mp = 0.3682cm.  Similarly, the nonlinear system showed improved performance with tr = 0.259775sec, ts = 1.325 sec, and Mp = 0.0734cm.
Keywords
Active Suspension Systems; Linear Systems; Nonlinear Systems; Quarter Car; PID control
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