## On Transfer Functions Limitations to Active Vehicle Suspension

Mathematical Modeling, Vol. 7 (2023), Issue 1, pg(s) 18-22

It is often assumed that if practical difficulties are neglected, active suspension systems could produce in principle arbitrary ideal behavior. This paper presents the factorization approach that is taken to derive limitations of achievable frequency responses to active vehicle suspension systems in terms of invariant frequency points and restricted rate of decay at high frequencies. The factorization approach enables the determination of complete sets of such constraints on various transfer functions from the load and road disturbances for typical choices of measured outputs and then chooses the optimal vector of the measurements from the point of view of the widest class of the achievable frequency responses. Using a simple linear two-degree-of-freedom car suspension model, it will be shown that even using complete state feedback and in the case in which the system is controllable in the control theory sense, there are still limitations to suspension performance in the fully active state.

## Disturbance rejection in a one-half vehicle suspension using a fuzzy controller

Trans Motauto World, Vol. 7 (2022), Issue 3, pg(s) 98-102

Generally, passenger ride comfort can be interpreted as an attenuation of sprung mass acceleration or as peak minimization of sprung mass vertical displacement, while good handling can be characterized as an attenuation of unsprung mass acceleration. This effort devoted to passive suspension design is ineffective because improvements to ride comfort are achieved at the expense of handling and vice versa. Instead, the best result can be achieved by active suspension, i.e. when an additional force can act on the system and simultaneously improve both of these conflicting requirements. Another important goal of the control design is to maintain robustness of the closed loop system. In the paper, fuzzy logic is used to simulate active suspension control of a one-half-car model. Velocity and acceleration of the front and rear wheels and undercarriage velocity above the wheels are taken as input data of the fuzzy logic controller. Active forces improving vehicle driving, ride comfort, and handling properties are considered to be the controlled actuator outputs. The controller design is proposed to minimize chassis and wheels deflection when uneven road surfaces, pavement points, etc. are acting on tires of running cars. As a result, a comparison of an active suspension fuzzy control and a spring/damper passive suspension is shown using MATLAB simulations.

## A design and stand tests of real-time vehicle active suspension

Trans Motauto World, Vol. 6 (2021), Issue 4, pg(s) 116-119

The paper deals with innovations in vehicle suspension technology developed in the Josef Bozek´s Research Center of Combustion Engines and Automobiles at CTU in Prague, Czech Republic. A unique innovative suspension system that uses a linear electric motor as a controlled actuator has been designed. Many experiments on the energy management in the system have been accomplished. In order to verify various control strategies and to test different ways of energy consumption optimization we designed and constructed a unique onequarter- car test stand. To realize simulation and practical experiments at the test stand it is necessary to find a proper experimental road disturbance signal to excite the active suspension system. The disturbance signal is applied on one more linear motor that is placed under a wheel of the one-quarter-car test stand to excite the active suspension system. The paper deals with the way and results of experimental verification of vehicle active suspension behavior when robust control is applied and also with energy management strategy that is used in the system. A modified H-infinity controller that enables to set energy management strategy is mentioned in the paper. At the close of the paper, some experiments taken on the one quarter-car model and their evaluation are discussed.

## On electromagnetic actuator control in the active suspension systems

Trans Motauto World, Vol. 5 (2020), Issue 1, pg(s) 6-9

In the paper, the design of a linear motor as an actuator in vehicle active suspension systems will be presented. The attention is focused on several interesting design aspects of a non-traditional actuator (a linear synchronous permanent magnet motor with electronic commutation) controlled to obtain a variable mechanical force for a car active suspension. The main advantage of such a solution is the possibility to generate desired forces acting between the unsprung (wheel) and sprung (car body) masses of the car, providing good insulation of the car sprung mass from the road surface disturbances. In addition, under certain circumstances it is possible to reduce or even eliminate the demands concerning the external power source.

## Energy control principles in an automotive active suspension system

Trans Motauto World, Vol. 4 (2019), Issue 3, pg(s) 107-110

In the paper, energy recuperation and management in automotive suspension systems with linear electric motors controlled using a proposed H∞ controller to obtain a variable mechanical force for a car damper is presented. Vehicle suspensions in which forces are generated in response to feedback signals by active elements obviously offer increased design flexibility compared to the conventional suspensions using passive elements such as springs and dampers. The main advantage of the proposed solution using a linear AC motor is the possibility to generate desired forces acting between the unsprung and sprung masses of the car, providing good insulation of the car sprung mass from the road surface disturbances. In addition, under certain circumstances using linear motors as actuators enables to transform mechanical energy of the vertical car vibrations to electrical energy, accumulate it, and use it when needed. Energy flow control (management) enables to reduce or even eliminate the demands concerning the external power source.

## Limitations to suspension performance in a two-degree-of-freedom car active suspension

Innovations, Vol. 7 (2019), Issue 3, pg(s) 111-114

It is often assumed that if practical difficulties are neglected, active systems could produce in principle arbitrary ideal behavior. This paper presents the factorization approach that is taken to derive limitations of achievable frequency responses for active vehicle suspension systems in terms of invariant frequency points and restricted rate of decay at high frequencies. The factorization approach enables us to determine complete sets of such constraints on various transfer functions from the load and road disturbance inputs for typical choices of measured outputs and then choose the “most advantageous” vector of the measurements from the point of view of the widest class of the achievable frequency responses. Using a simple linear two degree-of-freedom car suspension system model it will be shown that even using complete state feedback and in the case of in which the system is controllable in the control theory sense, there still are limitations to suspension performance in the fully active state.