Switched Adaptive Control of Air Handling Units With Discrete and Saturated Actuators

Abstract

This letter introduces a new switched adaptive control mechanism that can cope with parametric uncertainty while using discrete and saturated actuators. Control of air handling units (AHUs), where air and water supply have discrete and saturated characteristics, is the motivational drive behind this letter. We show that the cheap actuation and low computational requirements of building automation installations can be met after recasting the AHU thermal dynamics as a switched linear system with discrete working modes. Adaptive laws with antiwindup compensation and a switching law based on dwell time are introduced to cope with the uncertainties and input constraints of the switched linear system. Tracking performance is shown analytically and demonstrated via a numerical test case. Index Terms-Air handling units, switched adaptive control, input saturation, discrete input, dwell time. I. INTRODUCTION A T THE core of heating, ventilating and airconditioning (HVAC) systems in modern buildings are air handling units (AHUs), whose task is to provide air at desired temperature and humidity [1]-[3]. Considerable efforts have been made to provide efficient control for AHUs, where at least two intrinsic features of AHUs stand out [4]: first, the interaction between the air circuit and the water circuit in the heating/cooling coil gives rise to nonlinear dynamics; second, custom installation settings and variable operating conditions induce substantial uncertainty and several undetermined operating parameters. As a way to address nonlinearities and uncertainties, intelligent control techniques,

A Simultaneous Adaptation Law for a Class of Nonlinearly Parametrized Switched Systems

“…The objective is to track a desired trajectory defined as {q d l , q d u } = {2 sin(0.5t), sin(0.5t)}rad. Selection of K 11 = 170I, K 12 = 120I, K 21 = 25I, K 22 = 12I, Q 1 = Q 2 = 0.2I, κ = 0.9 yields the ADT ϑ * = 6.26sec according to (13). Therefore, a switching law σ(t) is designed as in Fig.…”

“…where µ ¯ M / m ; κ is a scalar defined as 0 < κ < where p (λ min (Q σ )/λ max (P σ )), min σ∈Ω ( p ). Theorem 1: Under Assumptions 1-2, the closed-loop trajectories of system (1) employing the control laws (7) and (10) with adaptive law (11) and switching law (13) are Uniformly Ultimately Bounded (UUB) if the gains α i and β i are designed as α i > max σ∈Ω ( σ /2) and β i > max σ∈Ω ( σ /2). Further, an ultimate bound b on the tracking error ξ can be found as…”

“…Following similar lines of proof recursively, one can conclude that V (t) < cµB for t ∈ [t l + T 1 ∞). This implies that once V (t) enters the interval [0, B], it cannot exceed the bound cµB any time later with the ADT switching law (13).…”

“…Switched systems represent an important class of hybrid systems consisting of subsystems with continuous dynamics together with a logic that orchestrates the switching action between them [1]- [9]. While some adaptive control approaches have been proposed to deal with the relevant problem of having parametric uncertainties in the subsystem dynamics ( [10]- [13] for linear and [14]- [18] for nonlinear subsystems), only few approaches, namely [17], [18], address some classes of uncertain switched systems whose subsystem dynamics have nonlinear in parameters (NLIP) form.…”

Adaptive hybrid synchronisation in uncertain Kuramoto networks with limited information

“…Also, some practical input constraints like input saturation or discrete inputs are of interest in view of: the limits of generation or load shedding, or some possibly discrete generation or load shedding actions [51]. An adaptive approach in this direction has been recently investigated in [52], even though the extension to network systems is open. Other networked-induced constraints like sampled information have been studied in [53], although adaptivity to parametric uncertainty has not been covered.…”