Simos A. Evangelou

Mechanical Steering Compensators for High- Performance Motorcycles

This paper introduces the idea of using mechanical steering compensators to improve the dynamic behavior of high-performance motorcycles. These compensators are seen as possible replacements for a conventional steering damper and comprise networks of springs, dampers, and a less familiar component called the inerter. The inerter was recently introduced to allow the synthesis of arbitrary passive mechanical impedances, and finds a potential application in the present work. The design and synthesis of these compensation systems make use of the analogy between passive electrical and mechanical networks. This analogy is reviewed alongside the links between passivity, positive reality, and network synthesis. Compensator design methods that are based on classical Bode-Nyquist frequency-response ideas are presented. Initial designs are subsequently optimized using a sequential quadratic programing algorithm. This optimization process ensures improved performance over the machine’s entire operating regime. The investigation is developed from an analysis of specific mechanical networks to the class of all biquadratic positive real functions. This aspect of the research is directed to answering the question: “What is the best possible system performance achievable using any simple passive mechanical network compensator?” The study makes use of computer simulations, which exploit a state-of-the-art motorcycle model whose parameter set is based on a Suzuki GSX-R1000 sports machine. The results show that, compared to a conventional steering damper, it is possible to obtain significant improvements in the dynamic properties of the primary oscillatory modes, known as “wobble” and “weave.” DOI: 10.1115/1.2198547

The stability of motorcycles under acceleration and braking

Abstract A comprehensive study of the effects of acceleration and braking on motorcycle stability is presented. This work is based on a modified version of a dynamic model presented earlier, and is thought to be the most comprehensive motorcycle dynamic model in the public domain. Extensive use is made of both non-linear and linearized models. The models are written in LISP and make use of the multibody modelling package AUTOSIM. There is novelty in the way in which control systems have been used to control the motorcycle drive and braking systems in order that the machine maintains desired rates of acceleration and deceleration. The results show that the wobble mode of a motorcycle is significantly destabilized when the machine is descending an incline or braking on a level surface. Conversely, the damping of the wobble mode is substantially increased when the machine is ascending an incline at constant speed, or accelerating on a level surface. This probably accounts for the pleasingly stable ‘feel’ of the machine under firm acceleration. Except at very low speeds, inclines, acceleration and deceleration appear to have little effect on the damping or frequency of the weave mode. Non-linear simulations have quantified the known difficulties to do with rear tyre adhesion in heavy braking situations that are dominated by rear wheel braking.

Control of motorcycle steering instabilities

The establishment of damper settings that provide an optimal compromise between wobble- and weave-mode damping is discussed. The conventional steering damper is replaced with a network of interconnected mechanical components comprised of springs, dampers and inerters - that retain the virtue of the damper, while improving the weave-mode performance. The improved performance is due to the fact that the network introduces phase compensation between the relative angular velocity of the steering system and the resulting steering technique

Multibody Aspects of Motorcycle Modelling with Special Reference to Autosim

Modelling of the ride and handling dynamics of motorcycles using the symbolic mechanical multibody system package Autosim has been carried out since 1995. Motorcycles are principally of tree structure but their geometry is complex in relation to the tyre to road contact and tyre force and moment descriptions and to the chain drive system. They may contain closed kinematic loops, according to common suspension and steering design variations. Various aspects of the modelling problem are discussed and some implications, from a multibody standpoint, of choosing different options are exposed. Simulation results illustrate the “antisquat” behaviour of a chain drive transmission and the “anti-dive” behaviour of a Telelever front suspension system.

Car driving at the limit by adaptive linear optimal preview control

The paper is concerned with modelling car drivers. The context of the work presented is explained. Then, previous research on the application of optimal linear preview control theory to driving road vehicles with only modest excursions from a straight-running equilibrium state is extended into the general large-lateral-motion arena. Optimal controls are found for steady-cornering trim states of an exemplary car at a given speed as a function of cornering effort, up to the practical limit. The manner in which the optimal controls change as the cornering vigour changes is discussed. Simulations of the virtual driver-controlled car are shown to demonstrate the closed-loop system following lateral path demands and the advantages of employing gain-scheduled adaptive control over a fixed-control scheme are demonstrated.

Motorcycle Steering Oscillations due to Road Profiling

A study of the effects of regular road undulations on the dynamics of a cornering motorcycle is presented. This work is based on an enhanced version of the motorcycle model described in ‘‘A Motorcycle Model for Stability and Control Analysis’’ (R. S. Sharp and D. J. N. Limebeer, 2001, Multibody Syst. Dyn., Vol. 6, No. 2, pp. 123 ‐142). We make use of root-locus and frequency response plots that were derived from a linearized version of this model; the linearization is for small perturbations from a general steady-cornering equilibrium state. The root-locus plots provide information about the damping and resonant frequencies of the key motorcycle modes at different machine speeds, while the frequency response plots are used to study the propagation of road forcing signals to the motorcycle steering system. Our results are based on the assumption that there is road forcing associated with both wheels and that there is a time delay between the front and rear wheel forcing signals—this is sometimes referred to as wheelbase filtering. As has been explained before, control systems are used in the nonlinear simulation code to establish and maintain the machine’s speed and roll angle at preset values (for flat road running). These controllers are used to find the machine’s equilibrium state and not to emulate a rider’s control actions. The results show that at various critical cornering conditions, regular road undulations of a particular wavelength can cause severe steering oscillations. At low speeds the machine is susceptible to road forcing signals that excite the lightly damped wobble and front suspension pitch modes. At higher speeds it is the weave and front wheel hop modes that become vulnerable to road forcing. We believe that the results and theory presented here explain many of the stability related road accidents that have been reported in the popular literature and are therefore of practical import. The models used in this research make use of the multibody modelling package AUTOSIM (Autosim 2.5 1 Reference Manual, 1998, Mechanical Simulation Corporation) and are available at the web site http://www.ee.ic.ac.uk/control/motorcycles/. The motorcycle and tire parameters can be found at the end of the code. @DOI: 10.1115/1.1507768#

Influence of Road Camber on Motorcycle Stability

This paper studies the influence of road camber on the stability of single-track road vehicles. Road camber changes the magnitude and direction of the tire force and moment vectors relative to the wheels, as well as the combined-force limit one might obtain from the road tires. Camber-induced changes in the tire force and moment systems have knock-on consequences for the vehicle’s stability. The study makes use of computer simulations that exploit a high-fidelity motorcycle model whose parameter set is based on a Suzuki GSX-R1000 sports machine. In order to study camber-induced stability trends for a range of machine speeds and roll angles, we study the machine dynamics as the vehicle travels over the surface of a right circular cone. Conical road surfaces allow the machine to operate at a constant steady-state speed, a constant roll angle, and a constant road camber angle. The local road-tire contact behavior is analyzed by approximating the cone surface by moving tangent planes located under the road wheels. There is novelty in the way in which adaptive controllers are used to center the vehicle’s trajectory on a cone, which has its apex at the origin of the inertial reference frame. The results show that at low speed both the weave- and wobble-mode stabilities are at a maximum when the machine is perpendicular to the road surface. This trend is reversed at high speed, since the weave- and wobble-mode dampings are minimized by running conditions in which the wheels are orthogonal to the road. As a result, positive camber, which is often introduced by road builders to aid drainage and enhance the friction limit of four-wheeled vehicle tires, might be detrimental to the stability of two-wheeled machines.

Advances in the modelling and control of series hybrid electric vehicles

Using a first-principles approach, the constituent components of a series hybrid electric car are modelled and integrated to form an overall coupled dynamic model. Controllers for the individual components are constructed, and are combined with a load follower supervisory controller and driver model to enable simulation of the vehicle under general operating conditions. The powertrain includes AC/DC, DC/AC and DC/DC converters which are described by standard average models with realistic power efficiencies. The powertrain also includes permanent magnet synchronous machines that are modelled using conventional d-q frame equations. There is novelty in the use of a general purpose friction moment, acting on each of the electrical machines, that is included to capture the equivalent energy loss due to friction, eddie currents and hysteresis, thus providing a good match between the predicted steady-state behaviour of the machines and experimental data. A longitudinal vehicle dynamics model with realistic descriptions for the tyres, aerodynamic resistance, suspension and continuously variable transmission (CVT) is also included. A scheme for improving the motor efficiency under general operating conditions, by controlling the CVT, is devised. The overall vehicle model is used to track the New European Drive Cycle (NEDC), for two design scenarios, one with fixed and one with variable final drive ratio. The simulation results demonstrate the applicability of the model for control system design, realistic prediction of vehicle behaviour and energy losses in the various components, and design optimisation.

Series Active Variable Geometry Suspension for Road Vehicles

A new family of electro-mechanical active suspensions that offers significant advantages with respect to passive and semiactive suspensions, while at the same time avoiding the main disadvantages of alternative active solutions, is presented in this paper. The series active variable geometry suspension takes a conventional independent passive or semiactive suspension as its starting point, and improves its behavior by actively controlling the suspension geometry with an electro-mechanical actuator. The advantages of this type of suspension are discussed and its simplest variant is studied in detail. Insight on the design process, as well as on the actuator modeling and selection is provided. Moreover, a control system for pitch attitude control of the chassis is presented. Simulation results obtained with a high-fidelity, full-vehicle, nonlinear model of a high-performance sports car that includes actuator dynamics and saturation limits are shown to confirm the potential of the proposed system.

Suppression of Burst Oscillations in Racing Motorcycles

Burst oscillations occurring at high speed, and under firm acceleration, can be suppressed with a mechanical steering compensator. Burst instabilities in the subject racing motorcycle are the result of interactions between the wobble and weave modes under firm-acceleration at high speed. Under accelerating conditions, the wobble-mode frequency (of the subject motorcycle) decreases, while the weave mode frequency increases so that destabilizing interactions can occur. The design analysis is based on a time-separation principle, which assumes that bursting occurs on time scales over which speed variations can be neglected. Even under braking and acceleration conditions linear time-invariant models corresponding to constant-speed operation can be utilized in the design process. The influences of braking and acceleration are modeled using d’Alembert-type inertial forces that are applied at the mass centers of each of the model’s constituent bodies. The resulting steering compensator is a simple mechanical network that comprises a conventional steering damper in series with a linear spring. In control theoretic terms, this network is a mechanical lag compensator. A robust control framework was used to optimize the compensator design because it is necessary to address the inevitable uncertainties in the motorcycle model, as well as the nonlinearities that influence the machine’s local behavior as the vehicle ranges over its operating envelope.