System identification and speed control of electro- mechanical dual acting pulley continuously variable transmission

Abstract

Researchers at Universiti Teknologi Malaysia (UTM) has designed, developed and patented an Electro-Mechanical Dual Acting Pulley Continuously Variable Transmission (EMDAP CVT). The newly developed EMDAP CVT is a complex nonlinear system. Since the system is difficult to be modeled, designing the suitable controller for the EMDAP CVT is a challenging task. However, it is possible to obtain model system and transfer function by employing System Identification (SI) technique. By having mathematical representation of the EMDAP CVT in form of transfer function, controller’s analysis and future works relating to the EMDAP CVT will be much easier. The main part of this research is to develop a model which is able to imitate the current EMDAP CVT system behaviours. Therefore, SI was performed to develop the model system and transfer function. Genetic Algorithm (GA) is used as an estimator with Nonlinear ARX (NARX) as a model structure. The mathematical modelling of the EMDAP CVT system is successfully presented and verified in form of 3rd order nonlinear transfer function. The focus of this research work is more on the implementation of speed control for the EMDAP CVT system based on model obtained from the SI. The EMDAP CVT speed controllers are designed for adjusting speed through providing appropriate CVT ratio to the system. The control objective is to achieve a desired output speed, which is used to specify and maintain the desired CVT ratio for the EMDAP CVT system. Proportional-Integral-Derivative (PID) controller is used as the basis and then fined tuned using conventional Ziegler-Nichols and Particle Swarm Optimization (PSO) method. Three controllers which are Proportional-plus-PSO (PPSO), Proportional-Derivative-plus-PSO (PD-PSO) and Proportional-Integral- Derivative-plus-PSO (PID-PSO) were developed to test the reliability of the obtained model system and transfer function. The performance of the designed controllers was demonstrated and validated through simulations and experiments. The error performance of the developed controllers is evaluated in terms of Integral of Absolute Error (IAE), Integral Square of Errors (ISE), Integral of Time multiplied by Absolute Errors (ITAE), and Mean Square Error (MSE). Based on the results, the PIDPSO speed controller gives a sufficient performance, such as settling time, overshooting and error performance. The validation approach resulted in lower than 5% percentage error thus verified the 95% confidence limit of the model system. Further controller’s analysis using Fuzzy Logic (FL) and Neural Network (NN) controllers were performed on the obtained model system and transfer function. The performance of the tested controllers were evaluated in terms of Steady State Error (SSE) and MSE values. All of the tested controllers produced good performance with steady state response within 5 seconds and SSE percentage lower than 5%. The end results show that, NARMA-L2 neural speed controller gives the best performance with SSE percentage of 0.91% and smallest MSE value of 3.28.