On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Critical Systems Theory: A Political Economy of Language, Thought, and Technology

An emergent form of political economy, facilitated by information and communication technologies (ICTs), is widely propagated as the apotheosis of unmitigated social, economic, and technological progress. Meanwhile, throughout the world, social degradation and economic inequality are increasing logarithmically. Valued categories of thought are, axiomatically, the basic commodities of the “knowledge economy”. Language is its means of exchange. This paper proposes a sociolinguistic method with which to critically engage the hyperbole of the “Information Age”. The method is grounded in a systemic social theory that synthesises aspects of autopoiesis and Marxist political economy. A trade policy statement is analysed to exemplify the sociolinguistically created aberrations that are today most often construed as social and political determinants.

Insights from ecological psychology and dynamical systems theory can underpin a philosophy of coaching

The aim of this paper is to show how principles of ecological psychology and dynamical systems theory can underpin a philosophy of coaching practice in a nonlinear pedagogy. Nonlinear pedagogy is based on a view of the human movement system as a nonlinear dynamical system. We demonstrate how this perspective of the human movement system can aid understanding of skill acquisition processes and underpin practice for sports coaches. We provide a description of nonlinear pedagogy followed by a consideration of some of the fundamental principles of ecological psychology and dynamical systems theory that underpin it as a coaching philosophy. We illustrate how each principle impacts on nonlinear pedagogical coaching practice, demonstrating how each principle can substantiate a framework for the coaching process.

Adaptive depth estimation in image based visual servo control of dynamic systems

This paper considers the question of designing a fully image based visual servo control for a dynamic system. The work is motivated by the ongoing development of image based visual servo control of small aerial robotic vehicles. The observed targets considered are coloured blobs on a flat surface to which the normal direction is known. The theoretical framework is directly applicable to the case of markings on a horizontal floor or landing field. The image features used are a first order spherical moment for position and an image flow measurement for velocity. A fully non-linear adaptive control design is provided that ensures global stability of the closed-loop system. © 2005 IEEE.

Flexible high-power multi DC-DC converters for train systems

This thesis reports on the investigations, simulations and analyses of novel power electronics topologies and control strategies. The research is financed by an Australian Research Council (ARC) Linkage (07-09) grant. Therefore, in addition to developing original research and contributing to the available knowledge of power electronics, it also contributes to the design of a DC-DC converter for specific application to the auxiliary power supply in electric trains. Specifically, in this regard, it contributes to the design of a 7.5 kW DC-DC converter for the industrial partner (Schaffler and Associates Ltd) who supported this project. As the thesis is formatted as a ‘thesis by publication’, the contents are organized around published papers. The research has resulted in eleven papers, including seven peer reviewed and published conference papers, one published journal paper, two journal papers accepted for publication and one submitted journal paper (provisionally accepted subject to few changes). In this research, several novel DC-DC converter topologies are introduced, analysed, and tested. The similarity of all of the topologies devised lies in their ‘current circulating’ switching state, which allows them to store some energy in the inductor, as extra inductor current. The stored energy may be applied to enhance the performance of the converter in the occurrence of load current or input voltage disturbances. In addition, when there is an alternating load current, the ability to store energy allows the converter to perform satisfactorily despite frequently and highly varying load current. In this research, the capability of current storage has been utilised to design topologies for specific applications, and the enhancement of the performance of the considered applications has been illustrated. The simplest DC-DC converter topology, which has a ‘current circulating’ switching state, is the Positive Buck-Boost (PBB) converter (also known as the non-inverting Buck-Boost converter). Usually, the topology of the PBB converter is operating as a Buck or a Boost converter in applications with widely varying input voltage or output reference voltage. For example, in electric railways (the application of our industrial partner), the overhead line voltage alternates from 1000VDC to 500VDC and the required regulated voltage is 600VDC. In the course of this research, our industrial partner (Schaffler and Associates Ltd) industrialized a PBB converter–the ‘Mudo converter’–operating at 7.5 kW. Programming the onboard DSP and testing the PBB converter in experimental and nominal power and voltage was part of this research program. In the earlier stages of this research, the advantages and drawbacks of utilization of the ‘current circulating’ switching state in the positive Buck-Boost converter were investigated. In brief, the advantages were found to be robustness against input voltage and current load disturbances, and the drawback was extra conduction and switching loss. Although the robustness against disturbances is desirable for many applications, the price of energy loss must be minimized to attract attention to the utilization of the PBB converter. In further stages of this research, two novel control strategies for different applications were devised to minimise the extra energy loss while the advantages of the positive Buck-Boost converter were fully utilized. The first strategy is Smart Load Controller (SLC) for applications with pre-knowledge or predictability of input voltage and/or load current disturbances. A convenient example of these applications is electric/hybrid cars where a master controller commands all changes in loads and voltage sources. Therefore, the master controller has a pre-knowledge of the load and input voltage disturbances so it can apply the SLC strategy to utilize robustness of the PBB converter. Another strategy aiming to minimise energy loss and maximise the robustness in the face of disturbance is developed to cover applications with unexpected disturbances. This strategy is named Dynamic Hysteresis Band (DHB), and is used to manipulate the hysteresis band height after occurrence of disturbance to reduce dynamics of the output voltage. When no disturbance has occurred, the PBB converter works with minimum inductor current and minimum energy loss. New topologies based on the PBB converter have been introduced to address input voltage disturbances for different onboard applications. The research shows that the performance of applications of symmetrical/asymmetrical multi-level diode-clamped inverters, DC-networks, and linear-assisted RF amplifiers may be enhanced by the utilization of topologies based on the PBB converter. Multi-level diode-clamped inverters have the problem of DC-link voltage balancing when the power factor of their load closes to unity. This research has shown that this problem may be solved with a suitable multi-output DC-DC converter supplying DClink capacitors. Furthermore, the multi-level diode-clamped inverters supplied with asymmetrical DC-link voltages may improve the quality of load voltage and reduce the level of Electromagnetic Interference (EMI). Mathematical analyses and experiments on supplying symmetrical and asymmetrical multi-level inverters by specifically designed multi-output DC-DC converters have been reported in two journal papers. Another application in which the system performance can be improved by utilization of the ‘current circulating’ switching state is linear-assisted RF amplifiers in communicational receivers. The concept of ‘linear-assisted’ is to divide the signal into two frequency domains: low frequency, which should be amplified by a switching circuit; and the high frequency domain, which should be amplified by a linear amplifier. The objective is to minimize the overall power loss. This research suggests using the current storage capacity of a PBB based converter to increase its bandwidth, and to increase the domain of the switching converter. The PBB converter addresses the industrial demand for a DC-DC converter for the application of auxiliary power supply of a typical electric train. However, after testing the industrial prototype of the PBB converter, there were some voltage and current spikes because of switching. To attenuate this problem without significantly increasing the switching loss, the idea of Active Gate Signalling (AGS) is presented. AGS suggests a smart gate driver that selectively controls the switching process to reduce voltage/current spikes, without unacceptable reduction in the efficiency of switching.

Experimental evaluation of position control methods for hydraulic systems

Presents a unified and systematic assessment of ten position control strategies for a hydraulic servo system with single-ended cylinder driven by a proportional directional control valve. We aim at identifying those methods that achieve better tracking, have a low sensitivity to system uncertainties, and offer a good balance between development effort and end results. A formal approach for solving this problem relies on several practical metrics, which is introduced herein. Their choice is important, as the comparison results between controllers can vary significantly, depending on the selected criterion. Apart from the quantitative assessment, we also raise aspects which are difficult to quantify, but which must stay in attention when considering the position control problem for this class of hydraulic servo systems.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Load compensation for systems with non-stiff source using state feedback

Various load compensation schemes proposed in literature assume that voltage source at point of common coupling (PCC) is stiff. In practice, however, the load is remote from a distribution substation and is supplied by a feeder. In the presence of feeder impedance, the PWM inverter switchings distort both the PCC voltage and the source currents. In this paper load compensation with such a non-stiff source is considered. A switching control of the voltage source inverter (VSI) based on state feedback is used for load compensation with non-stiff source. The design of the state feedback controller requires careful considerations in choosing a gain matrix and in the generation of reference quantities. These aspects are considered in this paper. Detailed simulation and experimental results are given to support the control design.

Vision based control for fixed wing UAVs inspecting locally linear infrastructure using skid-to-turn maneuvers

The following paper proposes a novel application of Skid-to-Turn maneuvers for fixed wing Unmanned Aerial Vehicles (UAVs) inspecting locally linear infrastructure. Fixed wing UAVs, following the design of manned aircraft, commonly employ Bank-to-Turn ma- neuvers to change heading and thus direction of travel. Whilst effective, banking an aircraft during the inspection of ground based features hinders data collection, with body fixed sen- sors angled away from the direction of turn and a panning motion induced through roll rate that can reduce data quality. By adopting Skid-to-Turn maneuvers, the aircraft can change heading whilst maintaining wings level flight, thus allowing body fixed sensors to main- tain a downward facing orientation. An Image-Based Visual Servo controller is developed to directly control the position of features as captured by onboard inspection sensors. This improves on the indirect approach taken by other tracking controllers where a course over ground directly above the feature is assumed to capture it centered in the field of view. Performance of the proposed controller is compared against that of a Bank-to-Turn tracking controller driven by GPS derived cross track error in a simulation environment developed to replicate the field of view of a body fixed camera.

Non-linear oscillations assessment of the distribution static compensator operating in voltage control mode

This article deals with the non-linear oscillations assessment of a distribution static comensator ooperating in voltage control mode using the bifurcation theory. A mathematical model of the distribution static compensator in the voltage control mode to carry out the bifurcation analysis is derived. The stabiity regions in the Thevein equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers are computed. The AC and DC capacitor impacts on the stability are analyzed through the bifurcation theory. The observations are verified through simulaation studies. The computation of the stability region allows the assessment of the stable operating zones for a power system that includes a distribution static compensator operating in the voltage mode.

Socioeconomic inequality profiles in physical and developmental health from 0-7 years : Australian National Study

Background: Early and persistent exposure to socioeconomic disadvantage impairs children’s health and wellbeing. However, it is unclear at what age health inequalities emerge or whether these relationships vary across ages and outcomes. We address these issues using cross-sectional Australian population data on the physical and developmental health of children at ages 0-1, 2-3, 4-5 and 6-7 years. Methods: 10 physical and developmental health outcomes were assessed in 2004 and 2006 for two cohorts each comprising around 5000 children. Socioeconomic position was measured as a composite of parental education, occupation and household income. Results: Lower socioeconomic position was associated with increased odds for poor outcomes. For physical health outcomes and socio-emotional competence, associations were similar across age groups and were consistent with either threshold effects (for poor general health, special healthcare needs and socio-emotional competence) or gradient effects (for illness with wheeze, sleep problems and injury). For socio-emotional difficulties, communication, vocabulary and emergent literacy, stronger socioeconomic associations were observed. The patterns were linear or accelerated and varied across ages. Conclusions: From very early childhood, social disadvantage was associated with poorer outcomes across most measures of physical and developmental health and showed no evidence of either strengthening or attenuating at older compared to younger ages. Findings confirm the importance of early childhood as a key focus for health promotion and prevention efforts.

Parallel linear system solution and its application to railway power network simulation

The Streaming SIMD extension (SSE) is a special feature embedded in the Intel Pentium III and IV classes of microprocessors. It enables the execution of SIMD type operations to exploit data parallelism. This article presents improving computation performance of a railway network simulator by means of SSE. Voltage and current at various points of the supply system to an electrified railway line are crucial for design, daily operation and planning. With computer simulation, their time-variations can be attained by solving a matrix equation, whose size mainly depends upon the number of trains present in the system. A large coefficient matrix, as a result of congested railway line, inevitably leads to heavier computational demand and hence jeopardizes the simulation speed. With the special architectural features of the latest processors on PC platforms, significant speed-up in computations can be achieved.

Control of aircraft for inspection of linear infrastructure

Inspection aircraft equipped with cameras and other sensors are routinely used for asset location, inspection, monitoring and hazard identification of oil-gas pipelines, roads, bridges and power transmission grids. This paper is concerned with automated flight of fixed-wing inspection aircraft to track approximately linear infrastructure. We propose a guidance law approach that seeks to maintain aircraft trajectories with desirable position and orientation properties relative to the infrastructure under inspection. Furthermore, this paper also proposes the use of an adaptive maneuver selection approach, in which maneuver primitives are adaptively selected to improve the aircraft’s attitude behaviour. We employ an integrated design methodology particularly suited for an automated inspection aircraft. Simulation studies using full nonlinear semi-coupled six degree-of-freedom equations of motion are used to illustrate the effectiveness of the proposed guidance and adaptive maneuver selection approaches in realistic flight conditions. Experimental flight test results are given to demonstrate the performance of the design.