Using feedback control to actively regulate the healing rate of a self-healing process subjected to low cycle dynamic stress

Abstract

Abstract. Intrinsic and extrinsic self-healing approaches through which materials can be healed generally suffer from several problems. One key problem is that to ensure effective healing and to minimise the propagation of a fault, the healing rate needs to be matched to the damage rate. This requirement is usually not met with passive approaches. An alternative to passive healing is active self-healing, whereby the healing mechanism and in particular the healing rate, is controlled in the face of uncertainty and varying conditions. Active self-healing takes advantage of sensing and added external energy to achieve a desired healing rate. To demonstrate active self-healing, an electrochemical material based on the principles of piezoelectricity and electrolysis is modelled and adaptive feedback control is implemented. The adaptive feedback control compensates for the insufficient piezo-induced voltage and guarantees a response that meets the desired healing rate. Importantly, fault propagation can be eliminated or minimised by attaining a match between the healing and damage rate quicker than can be achieved with the equivalent passive system. The desired healing rate is a function of the fault propagation and is assumed known in this paper, but can be estimated in practice through established prognostic techniques.

A material system with integrated fault diagnosis and feedback controlled self‐healing

“…Recent work has indicated the potential of this approach to tackle the second limitation. 33 The control subsystem also takes into account system uncertainties and disturbances during healing to ensure that the healing rate matches the estimated damage rate. In the present work a passive self-healing process whose healing mechanism is driven by piezoelectricity and electrolysis 34,35 is adopted to demonstrate the advantages of such an active self-healing system.…”

“…The self-healing model used is based on previous mathematical formulations. 33,39 The voltage V generated when a force f (t) is applied to an electromechanical material can be expressed using a state-space model equations expressed by ( 14) and (15).…”

“…The adaptive control design is based on a previous formulation. 33,39 First, the modeled self-healing mechanism ( 16) is redefined to include the adaptive control output U(t) to give (18). The input voltage to the polymer electrolyte is now the sum of the voltage V(t) created by the piezoelectric effect in response to the disturbance force and the additional adaptive feedback control voltage U(t).…”

“…43,44 𝜑 k are the POD mode (spatial basis function). They are fixed and must be orthonormal (32) and satisfy (33). The amplitude c k changes and is the signal used for detection and diagnosis.…”

“…This was highlighted in a previous publication. 33 As a solution to some of the challenges of passive self-healing, an active self-healing system was proposed. This combined the benefits of self-healing and feedback control to achieve a desired healing response capable of matching the damage rate.…”