INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control (2015) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/rnc.3475 Optimal transient performance under output set-point reset Leopoldo Jetto * ,† , Valentina Orsini and Raffaele Romagnoli Dipartimento di Ingegneria dell’Informazione, Università Politecnica delle Marche, Ancona, Italy SUMMARY The purpose of this paper is to propose a new method for the optimization of the output transition in the case of set-point reset for LTI, non-minimum phase, possibly non-hyperbolic plants. Assuming that the plant is stabilized by a proper feedback controller, the problem consists in finding a feedforward linear filter yielding a suitable reference trajectory for the closed-loop system. The approach situates in the framework of model pseudo-inversion because the external reference trajectory is computed starting from some desired features of the transient output between the two set points. A significant aspect of the new method is that the transition trajectory is not ‘ad hoc’ exactly prespecified by the designer. Rather, it is implicitly defined by the procedure for the minimization of a suitable multi-objective quadratic cost functional. As no pre-actuation is required, the method can be practically implemented on line and also works for the critical class of non-hyperbolic systems. Copyright © 2015 John Wiley & Sons, Ltd. Received 24 October 2014; Revised 7 October 2015; Accepted 8 October 2015 KEY WORDS: set-point tracking; transient optimisation; model stable pseudo inversion 1. INTRODUCTION While it is a a relatively simple task to attain an accurate transient tracking for minimum phase systems, inherent limitations on transient performance make the transient tracking problem much more involved in the case of non-minimum phase systems [1]. The theory of model stable inver- sion [2, 3] provides a valid framework to deal with the aforementioned problem and allows exact tracking through an infinite pre-actuation interval starting from null initial conditions. The practical unfeasibility of this solution motivated the use of approximated preview-based techniques with a bounded pre-actuation interval, see, for example, [4–10]. Over this interval, the pre-actuating input is required to drive the internal state from zero to the desired value, meanwhile keeping to zero the output response. All the aforementioned papers assume that the system is hyperbolic, namely without zeros on the boundary of the stability region. For systems with non-minimum phase zeros near the boundary of the stability region (near non-hyperbolic systems), the pre-actuation interval becomes very large and tends to infinite for zeros lying on the boundary (non-hyperbolic systems) [11]. With the purpose of removing some limitations inherent in the aforementioned techniques, a new stable pseudo-inversion approach has been recently proposed in [12–15]. In these references, the inverse problem consists in solving the convolution integral [12, 13, 15] (or the convolution sum in the case of sampled data systems [14]) with respect to the transient input, which minimizes the L 2 norm of the transient tracking error. The reference input is ‘a priori’ assumed to belong to the space of piece-wise continuously differentiable functions in [12, 13] or to the set of spline functions in [14, 15]. The assumed structure of the input guarantees an efficient solution of the optimization procedure and a sufficiently regular waveform of the reference input. *Correspondence to: Leopoldo Jetto, Dipartimento di Ingegneria dell’Informazione, Università Politecnica delle Marche, Ancona, Italy. † E-mail: l.jetto@univpm.it Copyright © 2015 John Wiley & Sons, Ltd.