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Research Papers

# Series Active Variable Geometry Suspension Robust Control Based on Full-Vehicle Dynamics

[+] Author and Article Information
Cheng Cheng

Department of Electrical and
Electronic Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: cheng.cheng12@imperial.ac.uk

Simos A. Evangelou

Mem. ASME
Department of Electrical and
Electronic Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: s.evangelou@imperial.ac.uk

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 21, 2018; final manuscript received November 22, 2018; published online January 14, 2019. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 141(5), 051002 (Jan 14, 2019) (14 pages) Paper No: DS-18-1086; doi: 10.1115/1.4042133 History: Received February 21, 2018; Revised November 22, 2018

## Abstract

This paper demonstrates the ride comfort and road holding performance enhancement of the new road vehicle series active variable geometry suspension (SAVGS) concept using an $H∞$ control technique. In contrast with the previously reported work that considered simpler quarter-car models, the present work designs and evaluates control systems using full-car dynamics thereby taking into account the coupled responses from the four independently actuated corners of the vehicle. Thus, the study utilizes a nonlinear full-car model that represents accurately the dynamics and geometry of a high performance car with the new double wishbone active suspension concept. The robust $H∞$ control design exploits the linearized dynamics of the nonlinear model at a trim state, and it is formulated as a disturbance rejection problem that aims to reduce the body vertical accelerations and tire deflections while guaranteeing operation inside the existing physical constraints. The proposed controller is installed on the nonlinear full-car model, and its performance is examined in the frequency and time domains for various operating maneuvers, with respect to the conventional passive suspension and the previously designed SAVGS $H∞$ control schemes with simpler vehicle models.

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## References

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## Figures

Fig. 1

Single-link variant of the SAVGS [8,9]: (a) Passive equilibrium position, in which the actuation torque TSAVGS=0 and (b) rotated configuration for nonzero TSAVGS

Fig. 2

Double-wishbone configurations of one corner (rear right) of the GT: (a) passive suspension configuration (left plot) in which the wheel has one degree-of-freedom with respect to the chassis via rotation of the wishbones, and (b) the extension of the passive suspension by employing the SAVGS (right plot). Points A, C, and G are attached to the chassis; points E and F are located on the spring-damper unit; and points B, D, H, and I are on the wheel. The lateral and vertical tire forces (i.e., 4Ftyne and 4Ftzne) are also shown.

Fig. 3

Global and local reference frames of full-car configuration in the xy plane

Fig. 8

General nonlinear full-car control scheme

Fig. 7

Bode plots of the full-car linearized model. The gains correspond to the nominal offset angle θSL(ne)=θSL(min)+ΔθSL(ne), when ΔθSL(ne)=90deg. The responses are from the inputs: vertical road speeds (first row), exogenous torques on the sprung mass (second row), and single-link angular speeds; to outputs: vertical acceleration, suspension deflection, and tire deflection at the rear-left wheel (first three columns), as well as pitching (fourth column) and rolling (fifth column) accelerations of the sprung mass of the GT.

Fig. 6

Magnitude bode plots (rear-left corner of vehicle) from single-link speed to (a) sprung mass acceleration, (b) suspension deflection, and (c) tire deflection as a function of frequency and nominal single-link angle, varied by ΔθSL(ne)

Fig. 10

H∞ control scheme. The weights at the inputs and outputs of the controller K∞ are absorbed into the final controller K (used in Fig. 8) by postmultiplication.

Fig. 5

PSD of the reference single-link velocity (θ˙SL3∗) and the tracked (actual) velocity (θ˙SL3) generated by the actuator when the vehicle is undergoing random road classes A and C

Fig. 4

Full-car model multibody structure [7]. The chassis, S, has 6DOFs with respect to the inertial reference frame. All the other bodies shown have only rotational DOFs, with labels x, y, and z used to designate the relative rotation between a body and its parent body. The remaining bodies are the lower wishbones (LWs), upper wishbones (UWs), hub carriers (AHCs and HCs), wheels (WHs), steering pinion (PIN), internal combustion engine (ICE), crown wheel (CRW), and differential gear (DFG). Virtual driver commands (steering, throttle, and brake) are shown with red arrows. Braking and tire shear forces are shown with thick black arrows, while parallel spring–damper arrangements represent suspension forces, vertical tire forces, and other forces in the powertrain and steering system. Kinematic constraints between bodies are denoted by dotted lines.

Fig. 9

Generalized bock diagram of H∞ control syntheses. The inputs d(s) and outputs z(s) of P are vector valued signals. Thecomponents of d(s) are the exogenous input disturbances. The components of z(s) are the performance variables of interest to be minimized in this work. The measurement signals that are used by controller K(s) are denoted by y(s) and the controlled inputs generated by the controller are denoted by u(s).

Fig. 12

Example PSDs for road profiles with roughness A and C considered in this work, shown in red and green lines, which correspond to good and poor quality roads. Gd is the displacement PSD as a function of spatial frequency, n. The classifications of roads A to H are defined in [ISO 8608:1995] [31].

Fig. 11

Singular value plot of the designed H∞ controller

Fig. 19

Responses at the rear-left wheel (a)–(d) and the rotational accelerations of the sprung mass (e) and (f), while the vehicle is traveling at a forward speed of 20 km/h and running over a smoothed bump of 0.05 m height and 2 m width at the left wheels. The passive suspension and SAVGS H∞-controlled system (F-SAVGS) are undergoing the same smoothed bump excitation.

Fig. 20

The boundaries of output torques versus single-link speeds' characteristics of the H∞ controlled SAVGS system (F-SAVGS) for simulations with random road C. i =1, 2, 3, and 4 match actuators in different corners of the vehicle corresponding to Fig. 3. The black envelope represents the actuator limit boundaries. Offsets between the mechanical powers and power constraints exist due to the power losses in the power electronics and actuators, which occur in the rolling bearings, gears (churning and meshing losses), and seals [7].

Fig. 13

Sprung mass vertical acceleration PSDs for each corner of the GT under random road class A

Fig. 14

Sprung mass vertical acceleration PSDs for each corner of the GT under random road class C

Fig. 15

Tire deflection PSDs for each corner of the GT under random road class C

Fig. 16

Pitching and rolling accelerations PSD plots at the mass center of the GT under random road class A

Fig. 17

Pitching and rolling accelerations PSD plots at the mass center of the GT under random road class C

Fig. 18

The 510 s time series simulation results under random road class A. The plots are (top to bottom) (1) road profile, (2) single-link angle, (3) vertical acceleration at the rear-right corner, (4) pitching acceleration of the sprung mass, and (5) rolling acceleration of the sprung mass.

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