Michael Cantoni

Control of Large-Scale Irrigation Networks

Irrigation networks of open-water channels are used throughout the world to support agricultural activity. By and large, these networks are managed in open loop. To achieve closed-loop water distribution management, it is necessary to augment these civil engineering systems with an appropriate information infrastructure-sensors, actuators, information processing, and communication resources. Recent pilot projects in Australia demonstrate the significant potential of closed-loop management, which can yield a significant improvement in the quality of service, while achieving improved water distribution efficiency. This paper focuses on the modelling and closed-loop control of open-water channels from the perspective of large-scale irrigation network management. Several feedback information structures are discussed and the key design tradeoffs identified

Systems engineering for irrigation systems: Successes and challenges

In Australia, gravity fed irrigation systems are critical infrastructure essential to agricultural production and export. By supplementing these large scale civil engineering systems with an appropriate information infrastructure, sensors, actuators and a communication network it is feasible to use systems engineering ideas to improve the exploitation of the irrigation system. This paper reports how classical ideas from system identification and control can be used to automate irrigation systems to deliver a near on-demand water supply with vastly improved overall distribution efficiency.

On Water-Level Error Propagation in Controlled Irrigation Channels

We consider the propagation of water-level errors in a controlled string of (identical) pools comprising an open-water irrigation channel. It is shown that water-level errors are amplified as they propagate upstream, whenever the feedback control scheme is decentralised and load-disturbance rejection is required in steady-state. Moreover, a design trade-off is identified between local performance, in terms of set-point regulation and load-disturbance rejection, and the error-propagation characteristics. The use of feed-forward/decoupling paths is considered in terms of managing this trade-off. However, the corresponding analysis suggests it is difficult to exploit the extra degree of freedom. Finally, we investigate a so-called distributed generalisation of the decentralised schemes. This leads to an optimal control based framework for dealing with the design trade-off.

Linear feedback systems and the graph topology

It is established for general linear systems that the gap metric induces the coarsest topology with respect to which both closed-loop stability and closed-loop performance are robust properties. In earlier works, similar topological results were obtained by exploiting the existence of particular coprime-factor system representations, not known to exist in general. By contrast, the development here does not rely on any specific system representations. Systems are simply characterized as subspaces of norm bounded input-output pairs, and the analysis hinges on the underlying geometric structure of the feedback stabilization problem. Unlike other work developed within such a framework, fundamental issues concerning the causality of feedback interconnections are discussed explicitly. The key result of this paper concerns the difference between linear feedback interconnections, with identical controllers, in terms of a performance/robustness related closed-loop mapping. Upper and lower bounds on the induced norm of this difference are derived, allowing for possibly infinite-dimensional input-output spaces and time-varying behavior. The bounds are both proportional to the gap metric distance between the plants, which clearly demonstrates the gap to be an appropriate measure of the difference between open-loop systems from the perspective of closed-loop behavior. To conclude, an example is presented to show that bounds of the form derived here for linear systems do not hold in a general nonlinear setting.

Robust Stability Analysis for Feedback Interconnections of Time-Varying Linear Systems

Feedback interconnections of causal linear systems are studied in a continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombes nu-gap metric and an integral-quadratic-constraint-based robust L2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz--Wiener--Hopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L2 input-output pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding Hankel operators are compact. These properties are first verified for stabilizable and detectable LTV state-space models to initially motivate the abstract formulation, and subsequently verified for frequency-domain multiplication by constantly proper Callier--Desoer transfer functions in analysis that confirms consistency of the developments with the time-invariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributed-parameter systems over a network with time-varying gains. (Less)

Detectability subspaces and observer synthesis for two-dimensional systems

The notions of input-containing and detectability subspaces are developed within the context of observer synthesis for two-dimensional (2-D) Fornasini-Marchesini models. Specifically, the paper considers observers which asymptotically estimate the local state, in the sense that the error tends to zero as the reconstructed local state evolves away from possibly mismatched boundary values, modulo a detectability subspace. Ultimately, the synthesis of such observers in the absence of explicit input information is addressed.

Robustness Analysis for Feedback Interconnections of Distributed Systems via Integral Quadratic Constraints

A framework is established for directly accommodating feedback interconnections of unstable distributed-parameter transfer functions in robust stability analysis via integral quadratic constraints (IQCs). This involves transfer function homotopies that are continuous in a ν -gap metric sense. As such, the development includes the extension of ν-gap metric concepts to an irrational setting and the study of uncertainty-set connectedness in these terms. The main IQC based robust stability result is established for constantly-proper transfer functions in the Callier-Desoer algebra; i.e. finitely many unstable poles and a constant limit at infinity. Problems of structured robust stability analysis and robust performance analysis are considered to illustrate use of the main result. Several numerical examples are also presented. These include stability analysis of an autonomous system with uncertain time-delay and a closed-loop control system, accounting for both the gain and phase characteristics of the distributed-parameter uncertainty associated with the nominal rational plant model used for controller synthesis.

A geometric theory for 2-D systems including notions of stabilisability

In this paper we consider the problem of internally and externally stabilising controlled invariant and output-nulling subspaces for two-dimensional (2-D) Fornasini–Marchesini models, via static feedback. A numerically tractable procedure for computing a stabilising feedback matrix is developed via linear matrix inequality techniques. This is subsequently applied to solve, for the first time, various 2-D disturbance decoupling problems subject to a closed-loop stability constraint.

Distributed controller design for open water channels

Abstract In the design of an automatic controller to achieve water-level set-point regulation and off-take load-disturbance rejection for an open water channel, a key concern is an inherent trade-off between local performance and the way water-level errors propagate due to control action. Here a structured optimal controller synthesis problem is formulated to systematically manage this trade-off, using H∞ loop-shaping ideas. The loop-shaping weights can be scalably designed and the imposed structure ensures the controller only involves local information exchange. Importantly, the distributed control structure we consider confines water-level error propagation to upstream pools, with corresponding benefits in terms of water distribution efficiency. Moreover, it coincides with the interconnection structure of a channel, and so the corresponding optimal synthesis problem has a convex characterisation; detailed state-space formulae are provided. Field test data are presented to illustrate overall performance.

On the formulation and solution of robust performance problems

A new approach to robust performance problems is proposed in this paper. The approach involves the optimisation of the so-called performance weights subject to a constraint, formulated in terms of the structured singular value, which ensures the existence of a stabilising feedback compensator that achieves robust performance with respect to the optimised performance weights and an uncertain plant set. Optimising over the performance weights in this way gives rise to an algorithm for systematically trading-off desired performance against specified plant uncertainty and performance limitations due to plant dynamics. The algorithm also yields a robust controller. The designer is only required to specify the uncertain plant set and an optimisation directionality, which is used to reflect desired closed-loop performance over frequency in terms of a corresponding cost function. Design of this directionality appears to be simpler than designing the performance weights directly.