Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Optimal control of nonlinear systems represented by differential algebraic equations

An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Optimal control of nonlinear differential algebraic equation systems

A novel iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified linear quadratic model based problem with parameter updating in such a manner that the correct solution of the original non-linear problem is achieved. The resulting algorithm has a particular advantage in that the solution is achieved without the need to solve the differential algebraic equations . Convergence aspects are discussed and a simulation example is described which illustrates the performance of the technique. 1. Introduction When modelling industrial processes often the resulting equations consist of coupled differential and algebraic equations (DAEs). In many situations these equations are nonlinear and cannot readily be directly reduced to ordinary differential equations.

Modelling human dynamics in-situ for rehabilitation and therapy robots

This paper outlines some rehabilitation applications of manipulators and identifies that new approaches demand that the robot make an intimate contact with the user. Design of new generations of manipulators with programmable compliance along with higher level controllers that can set the compliance appropriately for the task, are both feasible propositions. We must thus gain a greater insight into the way in which a person interacts with a machine, particularly given that the interaction may be non-passive. We are primarily interested in the change in wrist and arm dynamics as the person co-contracts his/her muscles. It is observed that this leads to a change in stiffness that can push an actuated interface into a limit cycle. We use both experimental results gathered from a PHANToM haptic interface and a mathematical model to observe this effect. Results are relevant to the fields of rehabilitation and therapy robots, haptic interfaces, and telerobotics

Calibration of closed loop controllers for setting impedances in force-reflecting systems

This paper discusses a new method of impedance control that has been successfully implemented on the master robot of a teleoperation system. The method involves calibrating the robot to quantify the effect of adjustable controller parameters on the impedances along its different axes. The empirical equations relating end-effector impedance to the controller's feedback gains are obtained by performing system identification tests along individual axes of the robot. With these equations, online control of end-effector stiffness and damping is possible without having to monitor joint torques or solving complex algorithms. Hard contact conditions and compliant interfaces have been effectively demonstrated on a telemanipulation test-bed using appropriate combinations of stiffness and damping settings obtained by this method.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Out of the ivory tower: the impact of wider social contact on the values, religious beliefs and identities of Chinese postgraduate students in the UK

This article explores the impact of wider social contact on the experience of Chinese postgraduate students of adaptation to life in the UK. Focus group and individual interviews were conducted with a group of 11 Chinese students on an MA programme at a university in southern England and individual interviews with three representatives of a local volunteer group (LVG) offering support to the Chinese students. Although it was perceived that the students’ support needs were not adequately met by the University, the additional support offered outside the University was unanimously valued and considered as enriching their cultural and linguistic experiences and meeting their expectations. However, frequent social contact with the LVG, whose members were mostly Christians, also had an impact on their values, religious beliefs and identities. In a discussion framed within the sociological perspective of proselytization or religious conversion and the broad framework of international education and globalization, the different responses to this contact are described in terms of believers, doubters, empathisers and commentators. Implications are considered for universities, people involved in providing social support for international students, and sponsors of international students.

Inverting recurrent neural networks for internal model control of nonlinear systems

In this paper, we show how a set of recently derived theoretical results for recurrent neural networks can be applied to the production of an internal model control system for a nonlinear plant. The results include determination of the relative order of a recurrent neural network and invertibility of such a network. A closed loop controller is produced without the need to retrain the neural network plant model. Stability of the closed-loop controller is also demonstrated.

Internal model control of nonlinear systems through the inversion of recurrent neural networks

Recurrent neural networks can be used for both the identification and control of nonlinear systems. This paper takes a previously derived set of theoretical results about recurrent neural networks and applies them to the task of providing internal model control for a nonlinear plant. Using the theoretical results, we show how an inverse controller can be produced from a neural network model of the plant, without the need to train an additional network to perform the inverse control.

Identification of nonlinear systems with a dynamic recurrent neural network

Two approaches are presented to calculate the weights for a Dynamic Recurrent Neural Network (DRNN) in order to identify the input-output dynamics of a class of nonlinear systems. The number of states of the identified network is constrained to be the same as the number of states of the plant.

Direct contact membrane distillation

This review looks at the work carried out over the past 15 years on membrane distillation and reports the conditions utilized for research. The process is still used mainly at the laboratory scale, but a few pilot plants have been built across the world, mostly for desalination and the production of potable water. Studies into membrane distillation have been concerned with the effect of mass transfer, heat transfer, and stirring rate, but the most important effect that has to be considered with this process is temperature polarization. A section on temperature polarization and the effect of boundary layers is included in this review.