Experimental feedback linearisation of a vibrating system with a non-smooth nonlinearity

Input-output partial feedback linearisation is demonstrated experimentally for the first time on a system with non-smooth nonlinearity, a laboratory three degrees of freedom lumped mass system with a piecewise-linear spring. The output degree of freedom is located away from the nonlinearity so that the partial feedback linearisation possesses nonlinear internal dynamics. The dynamic behaviour of the linearised part is specified by eigenvalue assignment and an investigation of the zero dynamics is carried out to confirm stability of the overall system. A tuned numerical model is developed for use in the controller and to produce numerical outputs for comparison with experimental closed-loop results. A new limitation of the feedback linearisation method is discovered in the case of lumped mass systems – that the input and output must share the same degrees of freedom.