Feedback linearisation of nonlinear vibration problems: A new formulation by the method of receptances

Experimental feedback linearisation of a non-smooth nonlinear system by the method of receptances

“…The stability of the zero dynamics can alternatively be verified using the receptance method with a describing function (DF) approach [21], either using an analytical DF (as in the present case) or by carrying out a series of slow-sweep amplitude-controlled sine-excitation tests. An exposition of the theory of feedback linearisation by the receptance method was recently presented by Zhen et al [22], and the purpose of the present paper is to demonstrate experimentally their findings, using the approach presented in that paper to replicate the closed-loop results already obtained for the three degrees of freedom test-rig with classical feedback linearisation by Lisitano et al [20].…”

“…The theory of feedback linearisation by the receptance method is given in detail by Zhen et al [22]. A summary is provided here for purposes of completeness.…”

“…The zero dynamics are those of the uncontrollable system (known as the internal dynamics) when the controlled degrees of freedom are set to zero. Zhen et al [22] showed that the zero dynamics were stable if, and only if, the poles of the transfer functioñ…”

“…Elements of the inverse receptance matrix (i.e. the experimental dynamic stiffness matrix) are required in equations (22) and (26) and shown in Figure 6, where inversion of both the measured and synthesised FRFs are shown to be in almost perfect agreement.…”

Cascade architecture for nonlinear control of transient and stationary regimes of friction-induced vibrations

“…More efficiency was shown for the PID when associated with the active force control (AFC) in [53]. Linear delayed and non-delayed state feedbacks were also proposed in [32,3,26,16,38] while nonlinear techniques exploiting the full and partially linearizing state feedbacks were exploited in [42,43] and combined with the receptance method in [11] for the active controlling of FIV. In [21], a control scheme which consists of a combination of a parallel feed-forward compensator (PFC) with an adaptive λ-tracking feedback control is proposed for controlling friction-induced self-excited oscillations in a two-mass electromechanical system with an elastic shaft and a friction load with a Stribeck effect.…”