Antiwindup for stable linear systems with input saturation: an LMI-based synthesis

By Gene Grimm, Jay Hatfield, Ian Postlethwaite, Andrew R. Teel, Matthew C. Turner, Luca Zaccarian. IEEE Transactions on Automatic Control, 2003

568 citations recorded by the source corpus.

This paper considers closed-loop quadratic stability and L/sub 2/ performance properties of linear control systems subject to input saturation. More specifically, these properties are examined within the context of the popular linear antiwindup augmentation paradigm. Linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification, called the "unconstrained closed-loop behavior." Building on known results on H/sub /spl infin// and LPV synthesis, the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem, which has an attractive system theoretic interpretation: the lower bound on the achievable L/sub 2/ performance is the maximum of the open and unconstrained closed-loop L/sub 2/ gains. In the special cases of zero-order (static) and plant-order antiwindup compensation, the feasibility conditions become (convex) linear matrix inequalities. It is shown that, if (and only if) the plant is asymptotically stable, plant-order linear antiwindup compensation is always feasible for large enough L/sub 2/ gain and that static antiwindup compensation is feasible provided a quasi-common Lyapunov function, between the open-loop and unconstrained closed-loop, exists. Using the solutions to the matrix feasibility problems, the synthesis of the antiwindup augmentation achieving the desired level of L/sub 2/ performance is then accomplished by solving an additional LMI.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e5977cff9a491d132ffae30fd8029912b6bea242

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In Control and Systems Engineering

Citations in the corpus

A new perspective on static and low order anti-windup synthesis (2004, background): “Both the works of Mulder et al. (2001) and those of Grimm et al. (2003) were successful at synthesizing compensators which yielded improved performance, International Journal of Control ISSN 0020–7179 print/ISSN 1366–5820 online # 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI:…”
Robust adaptive sliding mode attitude maneuvering and vibration damping of three-axis-stabilized flexible spacecraft with actuator saturation limits (2009, background): “Extensive results pertaining to spacecraft attitude control systems containing actuator saturation nonlinearities have been presented by Boskovi´ Li, and Mehra [8, 9], Tsiotras and Luo [17], Robinett et al. [18], Wallsgrove and Akella [19]; Yakoubi and Chitour [20], Xu and Lam [21], and Grimm et al.”
Saturated Adaptive Robust Control for Active Suspension Systems (2013, background): “To mention a few, in [14], the closed-loop quadratic stability and L2 performance properties of linear control systems subject to input saturation are considered, and these properties are examined within the context of the linear antiwindup augmentation paradigm.”
Exponential Control Barrier Functions for enforcing high relative-degree safety-critical constraints (2016, unknown): “A few control techniques to handle input and state-based constraints involve Model Predictive Control (MPC) [9], LMI optimizations [6], reference governors [3], [8], optimal control [10], [5], reachability analysis [10], [5], Barrier functions [17], [15], [16], [19], and other approaches [18], [6], ”