Published in IET Control Theory and Applications Received on 5th April 2007 Revised on 12th November 2007 doi: 10.1049/iet-cta:20070111 ISSN 1751-8644 Self-tuning control for active steering of a railway vehicle with solid-axle wheelsets H. Selamat 1 R. Yusof 2 R.M. Goodall 3 1 Electrical Engineering Faculty, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia 2 Centre for Artificial Intelligence and Robotics, Universiti Teknologi Malaysia, Jalan Semarak, 54100 Kuala Lumpur, Malaysia 3 Electronic and Electrical Engineering Department, Loughborough University, Leicestershire LE11 3TU, UK E-mail: hazlina@fke.utm.my Abstract: The instability caused by the conical (or profiled) shape of a solid-axle railway wheelset can be overcome by proper design of the vehicle’s primary suspension system but is generally difficult as some of the wheelset parameters, namely the conicity and creep coefficients, are time-varying. To maintain the wheelset stability at high speeds and satisfactory curving performance simultaneously over the whole range of the parameters’ variations, the self-tuning linear-quadratic regulator (S-T LQR) for the primary suspension system of a high-speed two-axle railway vehicle has been developed. The objective of the controller was to minimize the lateral displacement of the wheelset relative to track centerline and its yaw angle, on straight and curved tracks. The Continuous-time Least-Absolute Error with Variable Forgetting Factor (C-T LAE þ VFF) estimation algorithm has been used to estimate the wheelset parameters before being used in the calculation of the linear quadratic feedback control gain matrix. The simulation results show that the S-T LQR performed better than the fixed-gain LQR for both the conical and profiled wheelset, suggesting that the ability to estimate the time-varying wheelset parameters and use them in the feedback controller design is necessary to produce better primary suspension control performance. Nomenclature y F , y R , y B lateral displacement of front (leading), rear (trailing) wheelset and vehicle body c F , c R , c B yaw displacement front, rear wheelset and vehicle body v vehicle travel speed m, I wheelset mass (1250 kg) and yaw inertia (700 kg m 2 ) l, l B half gauge of wheelset (0.7 m) and half space of the vehicle body (4.5 m) r o , l wheel radius (0.45 m) and conicity m B , I B vehicle mass (30 000 kg) and yaw inertia (558 800 kg m 2 ) K l , C l lateral stiffness (200 kN/m) and damping (50 kN s/m) per wheelset f 11 , f 22 longitudinal and lateral creep coefficients R F , R R radius of the curved track at the front (leading) and rear (trailing) wheelsets u cF , u cR cant angle of the curved track at the front (leading) and rear (trailing) wheelsets y tF , y tR track lateral displacement (irregularities) at the front (leading) and rear (trailing) wheelsets u F , u R controlled torque input for the front (leading) and rear (trailing) wheelsets G gravity (9.8 m/s 2 ) 1 Introduction Solid-axle wheelset is the type of wheelset used in nearly all modern railway vehicles. It consists of two coned or profiled wheels rigidly connected by an axle so that both 374 IET Control Theory Appl., 2008, Vol. 2, No. 5, pp. 374–383 & The Institution of Engineering and Technology 2008 doi: 10.1049/iet-cta:20070111 www.ietdl.org