H∞ control and mathematical modeling of a quarter-car system via non-parametric approach

The experimental system that is used in this work is a custom-made MIMO electro-mechanical system which is constructed to be used in a project of The Scientific and Technological Research Council of Turkey (Number: 108E089). This system represents an active suspension system. Modeling and control applications are done for this system while taking the passenger comfort in an active suspension as the engineering problem. Initially passive suspensions, semi-active suspensions and active suspensions are examined and their mathematical models are presented. The mechanical characteristics of an active suspension's elements are explained. In the light of these information, characteristics of a spring-damper-mass mechanical system are inspected. Natural frequency and damping ratio concepts are reviewed. The mathematical modeling is done by using the Lagrange energy method and ensured by the modeling method which is based on Newton's second law. It is seen that the real parameters are different than the known label ones. At this point non-parametric system identification methods are included in order to tune these values. Frequency and transient response characteristics are gathered from the experimental system to gain an insight of it. Frequency response characteristics are found by a set of sine wave tests. A Bode-like graphic is presented and the natural frequency locations and damping effects are shown on it. As a result of applying these non-parametric methods, a modified mathematical model is found. A black-box parametric system modeling is done with the help of MATLAB's system identification toolbox and a 4th order state-space structured model is found. The required data are needed to be used in the parametric system identification algorithms and gathered from the experimental system by an experiment. The validities of the modified mathematical model and black-box model are compared and secured by checking the output results with the experimental system. In the control section, initially H_∞ norm of a system and H_∞ control theory are explained. Then H_∞ controllers are calculated for these three models (mathematical, tuned mathematical, black-box). With H_∞ controllers, the peak gains of a system are aimed to be reduced. The performance output is taken as the sprung mass acceleration and their peaks are a crucial factor that effects the passenger comfort in a vehicle. In the simulations, it is seen that the H_∞ controller successfully reduce the peaks of the performance output for each model. However there are some mechanical and electronic limitations for the experimental system and two of the calculated controllers clearly override them. The control law should be supplying a saturation that varies in the boundary of the actuator limits. The controller which is calculated for the black-box model satisfies the both limits and it is applied on the experimental system. Before starting the experiments, a second-order filter is designed and added to the performance output in order to apmlify certain frequencies, thus a more realistic behaviour is acquired. Experiments are done on the experimental system and it is seen that the H_∞ norm of the experimental system performance output is reduced. The simulations and experiments are done by using a randomized sine-wave sum input that represent a road test surface.