Output Regulation for Unknown Stable Linear Systems

Abstract

The regulation problem is addressed for single-input, single-output, linear unknown stable systems P (s), of unknown order, with exosystems generating biased multi-sinusoidal references and/or disturbances containing at most q known frequencies ω i , 1 ≤ i ≤ q. Sufficient conditions are presented which require the knowledge of sign[P (0)] and either sign{Re[P (jω i )]} or sign{Im[P (jω i )]}, 1 ≤ i ≤ q. The constructive proofs lead to the design of regulators with minimal order (2q + 1), provided that the gains are sufficiently small. For stable plants P (s) such that Re[P (jω)] > 0, for any ω ∈ R, a universal modular regulator is designed without gain limitations.

Robust control of flow separation over a pitching aerofoil using plasma actuators

“…so that the control problem can be formulated as a disturbance rejection problem, where the reference input v * = −η can be viewed as a disturbance vector, which matches the control input v (see Marino and Tomei, 2015). We aim at modifying the results in Marino and Tomei (2015) for our MIMO system (10), in the case of equal number of sensors n s and actuators n a , i.e., n p = n a = n s ≥ 1, where n p denotes the number of actuator/sensor pairs.…”

“…We aim at modifying the results in Marino and Tomei (2015) for our MIMO system (10), in the case of equal number of sensors n s and actuators n a , i.e., n p = n a = n s ≥ 1, where n p denotes the number of actuator/sensor pairs. Here,x ( j) a andx (i) s denote the position of the j-th actuator and the i-th sensor with respect to the chord length, respectively (see figure 1).…”

“…The key objective is to design v such that the closed-loop trajectories of system (10) are guaranteed to evolve within some "safe" invariant set in different scenarios, depending on uncertain parameters. To this aim, on the basis of the recent results in Marino and Tomei (2015), we design a robust output regulator guaranteeing exponential convergence of the regulation error: it only requires the system to have a non-zero steady-state gain of known sign.…”

“…Our objective is to solve the problem of directly controlling the unsteady flow separation using real-time velocity measurements, which are available in realistic applications (see, for example, Hanson et al, 2014;Segawa et al, 2010). We propose this flow separation problem as a practical application of the new theoretical results in Marino and Tomei (2015). In particular, we extend the simple SISO (Single-Input-Single-Output) robust output regulator presented in Marino and Tomei (2015) to MIMO (Multi-Input-Multi-Output) configurations.…”

“…We propose this flow separation problem as a practical application of the new theoretical results in Marino and Tomei (2015). In particular, we extend the simple SISO (Single-Input-Single-Output) robust output regulator presented in Marino and Tomei (2015) to MIMO (Multi-Input-Multi-Output) configurations. The aim of this paper is to show how, despite the high complexity of the system, a very simple robust output regulator is sufficient to effectively suppress the flow separation along an aerofoil, using DBD plasma actuators.…”