Erik Weyer

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

System identification of an open water channel

Abstract In this paper we derive models of the water level in an irrigation channel from system identification experiments. We present the complete system identification procedure from experiment design to model validation, taking into account prior physical information and that the intended use of the models is prediction and control. It is shown that a first order linear model captures the main trends in the data well, and together with prior information this model is probably sufficient for design of standard controllers. It is also shown that a higher order nonlinear model gives remarkably accurate predictions.

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.

Control of Irrigation Channels

Water losses in irrigation channels are large, but they can be substantially reduced by improving the control systems. The flows and water levels are controlled using overshot gates located along the channels, and in this paper we consider decentralized PI control and centralized multivariable LQ control of the flows and water levels. The controller designs are based upon simple system identification models which capture the relevant dynamics and are easy to use for control design. The controllers showed very good performance in field tests. The water levels recovered smoothly from disturbances without excessive oscillations, and the deviations from setpoints were small. As expected the centralized LQ controller showed better performance, attenuating disturbances faster than the PI controllers. However, more effort has to go into the design of an LQ controller.

LQ control of an irrigation channel

In this paper we consider LQ control of an irrigation channel in which the water levels are controlled using overshot gates located along the channel. Traditionally, irrigation channels have been modelled using the St. Venant equations which are partial differential equation, and hence quite difficult to use for control design. Here we base the design on simple system identification models which capture the relevant dynamics of the irrigation channel, and moreover they are easy to use for control design. It is shown that a quadratic criterion as minimised in LQ control makes sense for the physical control problem at hand. Auxiliary states are included in the state space model in order to achieve zero steady state error and to avoid inducing large waves. As expected, the LQ controller shows better performance than decentralised PI controllers. The water levels recover smoothly from disturbances without excessive oscillations, and the deviations from setpoints are small. Moreover the controller is robust against input uncertainties and unmodelled high frequency dynamics. However, much more effort has to go into the design of an LQ controller than of decentralised PI controllers, and whether the improved performance is worth the additional effort is something that has to be assessed on a case by case basis.

Grey box fault detection of heat exchangers

Abstract A grey-box model-based method for fault diagnosis is proposed in this paper. The method is based on a first principle model of the process unit, i.e. a heat exchanger, and on a grey-box model of the fault, i.e. the deterioration of the heat transfer surface by aging. During normal operating conditions the heat transfer coefficient is constant or slowly decreasing due to material settling on the heat transfer surface. In old heat exchangers big pieces of settled material can break off causing damage. When this happens, the heat transfer coefficients will rise sharply. In the proposed method a recursive least-squares estimator with forgetting factor is used to track the heat transfer coefficients. The settled material breakage fault is detected via detection of abrupt positive jump in the estimated heat transfer coefficients using a cumulative sum (CUSUM) test. The capability to detect faults in any industrial equipment is heavily dependent on the availability of suitable measurements. For heat exchangers the variables related to the in- and outflows of the equipment (flowrates and temperatures) are usually measured, but measurements along the equipment length are rarely available. Therefore, the possibilities of fault location in space are rather limited. However, simplified models can be used for fault detection in this case. Moreover, a fault detection method is proposed with the possibility of spatial fault location when measurements along the cold side are available. The proposed method is illustrated on simulated examples with different measurement situations.

Finite sample properties of system identification methods

In this paper we study the quality of system identification models obtained using the standard quadratic prediction error criterion for a general linear model class. The main feature of our results is that they hold true for a finite data sample and they are not asymptotic. The main theorems bound the difference between the expected value of the identification criterion evaluated at the estimated parameters and at the optimal parameters. The bound depends naturally on the model and system order, the pole locations, and the noise variance, and it shows that although these variables often do not enter in asymptotic convergence results, they do play an important role when the data sample is finite.

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.

Non-Asymptotic Confidence Sets for the Parameters of Linear Transfer Functions

We consider the problem of constructing confidence sets for the parameters of input-output transfer functions based on observed data. The assumptions on the noise affecting the system are reduced to a minimum; the noise can virtually be anything, but in return the user must be able to select the input signal. In this paper a procedure for solving this problem is developed in the general framework of leave-out sign-dominant confidence regions. The procedure returns confidence regions that are guaranteed to contain the true transfer function with a user-chosen probability for any finite data set.

Brief Finite sample properties of system identification of ARX models under mixing conditions

The asymptotic convergence properties of system identification methods are well known, but comparatively little is known about the practical situation where only a finite number of data points are available. In this paper we consider the finite sample properties of prediction error methods for system identification. We consider ARX models and uniformly bounded criterion functions. The problem we pose is: how many data points are required in order to guarantee with high probability that the expected value of the identification criterion is close to its empirical mean value. The sample sizes are obtained using generalisations of risk minimisation theory to weakly dependent processes. We obtain uniform probabilistic bounds on the difference between the expected value of the identification criterion and the empirical value evaluated on the observed data points. The bounds are very general, in particular no assumption is made about the true system belonging to the model class. Further analysis shows that in order to maintain a given bound on the difference, the number of data points required grows at most at a polynomial rate in the model order and in many cases no faster than quadratically. The results obtained here generalise previous results derived for the case where the observed data was independent and identically distributed.