| Steering system is one of the important systems, which directly relate to operability and safety of automobile. In recent years, due to its many advantages such as fuel economy, portability, environmental compatibility and compact size, the automobile EPS system has become a rapid development direction. The EPS system also has became a research hotspot and captured the extensive concern at domestic and overseas.The EPS system is a time varying, nonlinear, multi-input and multi-output system, the assistant control strategy of the EPS system which based on the traditional integer order model is not satisfying, including low robustness, poor anti-interference, bad rode feel and so on. So the modeling and control strategy of the EPS system play an important role in overall control performance. Because fractional mathematical model based on fractional calculus theory can describe the practical physical system more truly and objectively, and fractional-order controller has good robustness for mechanical nonlinearity, so fractional calculus has been introduced in automobile EPS system in this paper.The main research in this paper as follows:(1) Giving the characteristics, operating principal, research status of the EPS system at domestic and overseas; Mathematical model of EPS system has been set up which takes nonlinear tire model and two-degree freedom model of the vehicle into account; theoretical analysis of assist characteristic is carried out based on EPS system mathematical model.(2) Based on fractional calculus theory, with assistant motor in EPS system as the control object, building a high precision fitting fractional model of assistant motor by using optimization Oustaloup approximation algorithm. And fractional-order PI~?D~? controller is designed based on the fractional model, and use Particle Swarm Optimization algorithm to optimize and tune the parameters of fractional-order PI~?D~? controller.(3) The simulations about integer-order model, fractional-order model of the EPS system, fractional-order controller and integer-order controller are compared each other. And the road feel is also studied under fractional model. Simulation results show that the EPS fractional-order system under the control of fractional-order controller has better stability?robustness?anti-interference ability and road feel, and the control strategy can eliminate steering torque fluctuation effectively which is caused by the nonlinearity of the assistant motor. Availability of using fractional calculus theory to build fractional-order mathematical model of the EPS system and fractional-order assistant controller is verified.(4) One numerical algorithm of the fractional calculus dynamic equation based on the EPS system is given. According to linear and nonlinear state space equation of EPS fractional-order system, series solution of linear and nonlinear dynamic equation of the EPS system which contains fractional-order control item can be worked out, the precision and stability of system can be improved. Simulation results between the numerical algorithm and the Oustaloup approximation algorithm demonstrate consistency. Therefore, the availability of research work is verified in this paper. |
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