Robust multivariable control of complex biological processes

This paper addresses advanced control of a biological nutrient removal (BNR) activated sludge process. Based on a previously validated distributed parameter model of the BNR activated sludge process, we present robust multivariable controller designs for the process, involving loop shaping of plant model, robust stability and performance analyses. Results from three design case studies showed that a multivariable controller with stability margins of 0.163, 0.492 and 1.062 measured by the normalised coprime factor, multiplicative and additive uncertainties respectively give the best results for meeting performance robustness specifications. The controller robustly stabilises effluent nutrients in the presence of uncertainties with the behaviour of phosphorus accumulating organisms as well as to effectively attenuate major disturbances introduced as step changes. This study also shows that, performance of the multivariable robust controller is superior to multi-loops SISO PI controllers for regulating the BNR activated sludge process in terms of robust stability and performance and controlling the process using inlet feed flowrate is infeasible. (C) 2003 Elsevier Ltd. All rights reserved.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the best choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy. (C) 2004 Elsevier B.V. All rights reserved.

Practical scheme for error control using feedback

We describe a scheme for quantum-error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols [for example, Ahn Phys. Rev. A 65, 042301 (2001)], is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit flips. We also consider implementation in a solid-state quantum-computation architecture and estimate the maximal error rate that could be corrected with current technology.

Robust stability of sequential multi-input multi-output quantitative feedback theory designs

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

Predicting population dynamics of weed biological control agents: science or gazing into crystal balls?

Various factors can influence the population dynamics of phytophages post introduction, of which climate is fundamental. Here we present an approach, using a mechanistic modelling package (CLIMEX), that at least enables one to make predictions of likely dynamics based on climate alone. As biological control programs will have minimal funding for basic work (particularly on population dynamics), we show how predictions can be made using a species geographical distribution, relative abundance across its range, seasonal phenology and laboratory rearing data. Many of these data sets are more likely to be available than long-term population data, and some can be incorporated into the exploratory phase of a biocontrol program. Although models are likely to be more robust the more information is available, useful models can be developed using information on species distribution alone. The fitted model estimates a species average response to climate, and can be used to predict likely geographical distribution if introduced, where the agent is likely to be more abundant (i.e. good locations) and more importantly for interpretation of release success, the likely variation in abundance over time due to intra- and inter-year climate variability. The latter will be useful in predicting both the seasonal and long-term impacts of the potential biocontrol agent on the target weed. We believe this tool may not only aid in the agent selection process, but also in the design of release strategies, and for interpretation of post-introduction dynamics and impacts. More importantly we are making testable predictions. If biological control is to become more of a science making and testing such hypothesis will be a key component.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

Multi-robot control in highly dynamic, competitive environments

The control and coordination of multiple mobile robots is a challenging task; particularly in environments with multiple, rapidly moving obstacles and agents. This paper describes a robust approach to multi-robot control, where robustness is gained from competency at every layer of robot control. The layers are: (i) a central coordination system (MAPS), (ii) an action system (AES), (iii) a navigation module, and (iv) a low level dynamic motion control system. The multi-robot coordination system assigns each robot a role and a sub-goal. Each robot’s action execution system then assumes the assigned role and attempts to achieve the specified sub-goal. The robot’s navigation system directs the robot to specific goal locations while ensuring that the robot avoids any obstacles. The motion system maps the heading and speed information from the navigation system to force-constrained motion. This multi-robot system has been extensively tested and applied in the robot soccer domain using both centralized and distributed coordination.