Halfcar test setup for experimental nonlinear multivariable identification and control

The test setup is a scale model of the rear axis of a car suspension. This system was chosen because of it's industrial relevance with respect to control applications [2].

Figure 1 shows a picture of the developed test setup. The mass m_c represents the car body with inertia J_c. The suspension is modelled using 2 dampers, 2 springs and a mass m_s. The 2 wheels are represented by 2 springs and 2 masses m_wl and m_wr. The road displacement is enforced by 2 hydraulicly actuated pistons (not shown in figure 1).

The system has 4 inputs:

• two active: left and right piston displacements (0 - 0.1m) and
• two semi-active: viscosity of magneto-rheological dampers (0 - 1.5V).

The maximum velocity of the pistons (figure 2) is determined by the flow rate of the pump and is about 1m/s. The position of the pistons, measured with an integrated magneto-strictive sensor, is controlled using a PID controller and a servo valve. The bandwidth is about 30Hz with a slight overshoot at 25Hz.

The semi-active dampers [3] are a product of LORD Corporation, type RD-1097-01. The damper is filled with a magneto-rheological fluid. The damping characteristic can be altered by changing the magnetic field around the fluid. This magnetic field is determined by sending a current to the damper. The current in its turn is controlled by a voltage between 0V and 1.5V.

To control the test setup a dSpace DS1104 system is used. Combined with Matlab/Simulink and ControlDesk, this system allows us to apply arbitrary signals to all 4 inputs simultaneously.

The system has 10 sensors (indicated in figure 1):

• accelerations at the left and right side of mass m_c,
• forces passing through the suspension left and right,
• compression of the left and right damper,
• displacement of the masses m_s and m_c and
• position of the left and right piston.

The displacements of the 2 masses as well as the compression of the left and right damper are measured using Baumer Electric laser displacement sensors. Type OADM 12I6460/S35Ais used for the compression of the dampers and type OADM 20I6472/S14F for the displacement of the 2 masses.

All the measurements as well as the control loop for the displacement of the left and right piston are done at 2kHz. Due to a limitation of the measurement system only 8 sensors can be measured simultaneously.

Figure 3 shows a schematic representation of the test setup. The figure introduces a terminology to refer to the different parts and motions of the test setup in a uniform and consistent way:

• the subscript l refers to the left side, r to the right side
• the subscript w refers to the wheel, s to the suspension, d to the damper, b to the suspension linkage bar, g to the center of gravity and c to the car body
• m_wl, m_wr, m_s, m_c and J_c refer to the corresponding inertia's
• x_wl, x_wr, x_s, x_c, x_cl, x_cr, x_g, q_s and q_c refer to the corresponding displacements and rotations
• F_wl, F_wr, F_bl, F_br, F_sl, F_sr, F_dl and F_dr refer to the forces passing through the corresponding elements
• F_fs and F_fc refers to the friction force in the corresponding linear guide.

The spring stiffness as mentioned on the data sheet are for the left and right wheel spring 11700N/m and for the left and right suspension spring 3790N/m. The data sheet for the dampers can be found here. Some modelling of a magneto-rheological damper has been done in [4] and damper characteristics are shown in [3]. The masses are not known.

1. J. Schoukens, J.G. Nemeth, P. Crama, Y. Rolain, R. Pintelon; Fast Approximate Identification of Nonlinear Systems; Automatica, nr. 39, pp. 1267-1274, 2003.
2. J. De Cuyper, D. Coppens, C. Liefooghe, J. Swevers, M. Verhaegen; Advanced Drive File Development Methods for Improved Service Load Simulation on Multi Axial Durability Test Rigs, Proc. of the International Acoustics and Vibration Asia Conference, Singapore, pp. 339-354, 1998.
3. M.J. Chrzan, J.D. Carlson; MR Fluid Sponge Devices and their use in Vibration Control of Washing Machines; Proc. SPIE Vol. 4331, p. 370- 378, Smart Structures and Materials 2001: Damping and Isolation.
4. S.M. Savaresi, S. Bittanti, M. Montiglio; Identification of Semiphysical and Black-box Nonlinear Models: the case of MR-dampers for Vehicles Control; Automatica, nr. 41, pp. 113-127, 2004.