Research
Research
For input redundant systems, it is possible to construct distinct inputs producing identical outputs, from the same initial state. Thus, a system is input redundant if it is not left-invertible. We propose a rigorous framework to support this new definition referring to signals. From the observation that state trajectories induced by the two inputs can be identical or not, we designed an enriched taxonomy of input redundancy. A comprehensive set of characterizations based on geometric control theory is associated with the proposed definitions and we also conceived a degree of redundancy. This allows to carry out a thorough comparison with the state-of-the-art. Finally, the fact that over-actuated systems are input redundant is formally proved. This fact leads to a control design framework which can easily cope with over-actuated systems equipped with dynamical actuators.
By directly referring to signals, our definition readily applies to any input-to-output mapping. As an illustration of the potentiality, we also tackle the case where input and state constraints are imposed on the system. This context is indeed of foremost importance since input redundancy has been historically regarded as a way to deal with input saturations. Based on an example illustrating how constraints can challenge redundancy, we highlight a more complex phenomenology. This motivates the enrichment of the existing framework on redundancy. Then, we derived a sufficient condition for redundancy to be preserved when imposing constraints in the most general context of arbitrary constraints. It is shown that redundancy can be destroyed only when input and state trajectories lie on the border of the set of constraints almost all the time. Finally, those results are specialized and expanded under the assumption that input and state constraints are linear.
Then, we derive the notion of input redundancy in the context of:
Linear Parameter Dependent (LPD) systems by proposing sufficient conditions for such a system to be adaptive or robust input redundant, depending on whether the parameters are known or not.
Switched systems by focusing on the continuous input. Our approach initially involves transforming the switched linear system into a linear system depending polynomially on a univariate parameter through Lagrange polynomial interpolation. This allows us to leverage recent results in geometric control theory and input redundancy for parameter-dependent systems, and adapt them to the context of switched systems in order to obtain the desired conditions.
The parallel interconnection of power converters feeding a common load is a valuable topology in many application such as microgrids. Based on our research on input redundancy, we can clearly show that such a system is input redundant. In practical terms, the main control objective, related to the voltage regulation of the load does not determine all of the input and state trajectories. The degrees of freedom left are in fact related to the current distribution on the converters, namely the current sharing. We propose several control allocation methods, tailored for the interconnected power converters to enhance performances and reliability. In particular, these methods use the redundancy to meet an on-line optimal current distribution among the converters without impacting the voltage regulation. Theoretical interpretation is provided by relying on (i) geometric control tools, such as controlled invariant and output invisible subspaces or (ii) energy conversvatife quantities (Casimir functions) in the Hamiltonian framework. State and input constraints can be taken in to account and an interesting by-product of our approaches is the ability to put converters in and out of service through trivial adjustments of the code. Experimental results assess the benefits of the proposed methods.
For input reundant system, control allocation methods have been proposed to deal with the degrees of freedom in a way that the performance output is left unchanged. It is of particular interest when the main control objective requires precision. However, this decoupling between the degrees of freedom and the performance output can be destroyed by input constraints. In this context, we show that a mere unilateral coupling can still be achieved using a novel control structure.