Robust Hybrid PI Controller with a Simple Adaptation in the Integrator Reset State

Scola, Ignácio Rubio; Quadros, Mariella Maia; Leite, Valter J. S.

doi:10.1016/j.ifacol.2017.08.290

Cited by 6 publications

(1 citation statement)

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“…Note that the reset controller reduced the overshoot and shortened the settling time significantly while preserving the rise time at a value almost identical to that of the LTI controller. This transient performance improvement is one of the favorable properties of reset control systems, as resetting control input eliminates the acceleration on the outputs at appropriate instants, reducing the overshoot and settling time, see References 4,26‐29. The

{\mathscr{H}}_2

norm obtained by numerical integration (i.e.,

\sqrt{\int_{t_0}^{t_f}z{(t)}^Tz(t) dt}

) was 1.59 for the reset controller, which was 10.89% smaller than that of the LTI controller.…”

Section: Numerical Examplementioning

confidence: 99%

ℋ2 reset controller design for linear systems using piecewise quadratic Lyapunov functions

Ban

Seo

Kim

et al. 2023

Intl J Robust & Nonlinear

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This study presents reset controller design conditions for multiple-input and multiple-output (MIMO) linear systems in terms of linear matrix inequalities (LMIs). The design conditions were developed using a piecewise quadratic Lyapunov function (PWQLF), leading to less conservative conditions than using a common Lyapunov function. Achieving LMI relaxation of the PWQLF-based reset controller design conditions for MIMO linear systems is challenging because (1) dividing the flow set of the reset condition is highly complex, (2) equality constraints, which make the PWQLF continuous on the boundaries between adjacent flow sets, prevent the use of congruence transformation in matrix inequalities, and (3) indefiniteness of the matrices for regional constraints also makes it difficult to apply standard LMI relaxation techniques. To overcome these difficulties, this study introduces a two-dimensional projection of the plant's output measurements and reset controller's states to construct a reset condition, allowing the PWQLF to be tractable in MIMO linear systems. Then, a new stability analysis condition is derived using the elimination lemma, overcoming the challenges in LMI relaxation of the controller design attributed to the equality constraints and indefinite matrices. An LMI-based reset controller design condition is then proposed based on the proposed stability analysis. To account for transient behavior,  2 tracking reset controller design problem is addressed. A numerical example is provided to demonstrate the effectiveness of the proposed method.

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