EACS 2016 paper - Active control of a non-smooth nonlinear system using feedback linearisation

<div>EACS 2016 Paper No. 148</div><div><br></div>Partial feedback linearisation is applied to an experimental nonlinear non-smooth mechanical system with three degrees of freedom and opening and closing gaps to produce a piecewise-linear stiffness characteristic. Stepped sine testing shows that the second mode is strongly affected by the nonlinearity whereas the first and third modes remain essentially linear. A mathematical model is tuned to accurately reproduce the nonlinear test behaviour, including jump phenomena. The classical theory of feedback linearisation is then briefly reviewed and feedback gains are determined based on the tuned model with the purpose of pole assignment. The zero dynamics are found to be stable. Closed-loop tests are carried out to assign linear viscous damping ratios to the linearised system. These are measured using the logarithmic decrement and found to be in very good agreement with demanded values.