Showing papers by "Richard H. Middleton published in 2007"

Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels

Abstract: There has recently been significant interest in feedback stabilization problems with communication constraints including constraints on the available data rate. Signal-to-noise ratio (SNR) constraints are one way in which data-rate limits arise, and are the focus of this paper. In both continuous and discrete-time settings, we show that there are limitations on the ability to stabilize an unstable plant over a SNR constrained channel using finite-dimensional linear time invariant (LTI) feedback. In the case of state feedback, or output feedback with a delay-free, minimum phase plant, these limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity data rate over the same channel. In the case of LTI output feedback, additional limitations are shown to apply if the plant is nonminimum phase. In this case, we show that for a continuous-time nonminimum phase plant, a periodic linear time varying feedback scheme with fast sampling may be used to recover the original SNR requirement at the cost of robustness properties. The proposed framework inherently captures channel noise effects in a simple formulation suited to conventional LTI control performance and robustness analysis, and has potential to handle time delays and bandwidth constraints in a variety of control over communication links problems.

On the Achievable Delay Margin Using LTI Control for Unstable Plants

Abstract: Handling delays in control systems is difficult and is of long-standing interest. It is well known that, given a finite-dimensional linear time-invariant (FDLTI) plant and controller forming a strictly proper stable feedback connection, closed-loop stability will be maintained under a small delay in the feedback loop, although most closed loop systems become unstable for large delays. One previously unsolved fundamental problem in this context is whether, for a given FDLTI plant, an arbitrarily large delay margin can be achieved using LTI control. Here, we adopt a frequency domain approach and demonstrate that, for a strictly proper real rational plant, there is a uniform upper bound on the delay that can be tolerated when using an LTI controller, if and only if the plant has at least one closed right half plane pole not at the origin. We also give several explicit upper bounds on the achievable delay margin, and, in some special cases, demonstrate that these bounds are tight.

Stabilization with disturbance attenuation over a Gaussian channel

Abstract: We propose a linear control and communication scheme for the purposes of stabilization and disturbance attenuation when a discrete Gaussian channel is present in the feedback loop. Specifically, the channel input is amplified by a constant gain before transmission and the channel output is processed through a linear time invariant filter to produce the control signal. We show how the gain and filter may be chosen to minimize the variance of the plant output. For an order one plant, our scheme achieves the theoretical minimum taken over a much broader class of compensators.

The 2006 NUbots Team Report

Abstract: At RoboCup 2004 in Lisbon the NUbots successfully defended their 3rd placing for the second year running, having first entered the competition in 2002. Once again, the NUbots only lost one game in the entire tournament: this time to the German Team who went on to win the competition. The introduction of the Sony aibo ERS-7 robot led to considerable attention being paid to the porting of code. As a result we were unable to spend as much time implementing new ideas and approaches. The NUbots also had a smaller development team than in previous years which further hampered the design and implementation of new methods. It should also be noted that the NUbots are intending to perform complete rewrite for 2005. For this reason, this team report will focus on the new features of the system and the changes made to accommodate the new robot. Further information on our current/past system can be found in our 2003 [1] and 2002 [2] reports.

Output Feedback Sensitivity Functions Under Signal to Noise Ratio Constraint

Abstract: We analyse the control output feedback sensitivity function which results from imposing the minimal signal-to-noise ratio requirement needed for stabilisability. The signal to noise ratio constraint used here includes the effect of a band limited, additive coloured Gaussian noise communication link and a (non) minimum phase unstable continuous (discrete) linear time invariant (LTI) plant with time delay. Target performance is introduced in a form that directly implies an additional term in the required SNR compared to the case of stabilisability only. In a first approach performance is sought as output disturbance rejection giving guaranteed reference tracking at zero frequency (integral action) and compensation for perturbations over a range of frequencies. It is noted that the resulting additional cost can be made vanishingly small by making the closed loop arbitrarily slow. In a second approach we define frequency bounds for the magnitude of the output sensitivity function. These bounds will guarantee low error reference tracking and rejection of disturbances over a non trivial range of frequencies. Based on this, a lower bound for the required extra SNR that satisfies the mentioned sensitivity magnitude bounds is proposed and its tightness discussed.

Practical implementation of a narrowband high frequency distributed model for locating partial discharge in a power transformer

Abstract: This paper proposes the use of a narrowband high frequency based distributed transformer model for estimating partial discharge location within the winding of an interleaved power transformer. At high frequencies, the residual inductance within a transformer winding becomes significant This inductive interaction generates its own characteristic response which, due to its distributed nature, can be utilized for partial discharge location. The technique proposed here takes advantage of the high frequency nature of a partial discharge and requires measurement at one location only. It also does not require detailed knowledge of the transformer's physical and material specifications. To confirm this approach, practical tests were conducted on a 66 kV/25 MVA interleaved transformer winding. The partial discharge injection was delivered by an oil immersed point-plane 7.5 kV source with the data captured using a current probe on the earth terminated neutral.

A narrowband high frequency distributed power transformer model for partial discharge location

Abstract: This paper utilises a narrow band high frequency distributed transformer model to estimate partial discharge location. Here a narrow band of frequencies within the frequency response of the system, that exhibit resonant pole behaviour, is specifically targeted. It is proposed that the observed response is due to the interaction of residual winding inductance with capacitance to ground. This physical phenomenon is inherently distributed; hence regions within the frequency response related to this interaction will be dependent upon the input location. With this premise an algorithm that estimates the location of the partial discharge by iteratively comparing the proposed model at various locations within the winding with the observed partial discharge frequency response is implemented. The algorithm was tested on a single phase of a 66 kV/25 MVA interleaved transformer winding where the partial discharge was injected via an oil immersed point-plane 7.5 kV source.

On AIMD Congestion Control in Multiple Bottleneck Networks

Abstract: We consider a linear algebraic model of the Additive-Increase Multiplicative-Decrease congestion control algorithm and present results on average fairness and convergence for multiple bottleneck networks. Results are presented for networks of both long-lived and short-lived flows.

A reactive approach for mining project evaluation under price uncertainty.

Abstract: Projects in the mining industry are undertaken with the objective of maximizing economic value, which is near-universally measured by the Net Present Value (NPV), considering all capital expenditure and operating cash flow. This industry is usually considered high risk because of historically volatile commodity prices (directly impacting revenues) and the fact that very large capital expenditures are required upfront for the construction of processing, mining and transport infrastructure. In order to optimize overall investment returns in a mining project, it is thus essential to use the best possible project valuation method so that the sizing of initial capital expenditures are appropriate to the expected returns and risks. A commonly used method for mining project evaluation calculates the expected NPV of a mine plan based upon the expected future commodity price given the current spot price. This method often undervalues a mining project since it ignores future price uncertainty and does not allow for managerial flexibility or optionality. This paper presents an alternate approach to mining project evaluation – the “reactive” approach. This “reactive” approach emulates a strategy that a real operating mine would undertake over its mine life by modifying the mine plan in each new period in response to the latest information on metal price. This paper also demonstrates that the “reactive” approach can estimate the mine project value more accurately by recognizing additional value due to the presence of management flexibility and optionality.