On the time delay in continuous in-cylinder sampling from IC engines

When gas sample is continuously drawn from the cylinder of an internal combustion engine, the sample that appears at the end of the sampling system corresponds to the in-cylinder content sometime ago because of the finite transit time which is a function of the cylinder pressure history. This variable delay causes a dispersion of the sample signal and makes the interpretation of the signal difficult An unsteady flow analysis of a typical sampling system was carried out for selected engine loads and speeds. For typical engine operation, a window in which the delay is approximately constant may be found. This window gets smaller with increase in engine speed, with decrease in load, and with the increase in exit pressure of the sampling system.

A perturbation approach to the stabilization of nonlinear cascade systems with time-delay

The effect of bounded input perturbations on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability is preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. These results are used to study the stabilization of partially linear cascade systems with partial state feedback.

Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

Model-based control of a Rijke tube combustion instability

A Rijke tube is used to demonstrate model-based control of a combustion instability, where controller design is based on measurement of the unstable system. The Rijke tube used was of length 0.75m and had a grid-stabilised laminar flame in its lower half. A microphone was used as a sensor and a loudspeaker as an actuator for active control. The open loop transfer function (OLTF) required for controller design was that from the actuator to the sensor. This was measured experimentally by sending a signal with two components to the actuator. The first was a control component from an empirically designed controller, which was used to stabilise the system, thus eliminating the non-linear limit cycle. The second was a high bandwidth signal for identification of the OLTF. This approach to measuring the OLTF is generic and can be applied to large-scale combustors. The measured OLTF showed that only the fundamental mode of the tube was unstable; this was consistent with the OLTF predicted by a mathematical model of the tube, involving 1-D linear acoustic waves and a time delay heat release model. Based on the measured OLTF, a controller to stabilise the instability was designed using Nyquist techniques. This was implemented and was seen to result in an 80dB reduction in the microphone pressure spectrum. A robustness study was performed by adding an additional length to the top of the Rijke tobe. The controller was found to achieve control up to an increase in tube length of 19%. This compared favourably with the empirical controller, which lost control for an increase in tube length of less than 3%.

Low-order modelling of ducted flames with temporally varying equivalence ratio in realistic geometries

The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the socalled G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies. Copyright © 2011 by ASME.

Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy. © 2013 Copyright Taylor and Francis Group, LLC.

Delayed control of a Moore-Greitzer axial compressor model

Several feedback control laws have appeared in the literature concerning the stabilization of the nonlinear Moore-Greitzer axial compression model. Motivated by magnitude and rate limitations imposed by the physical implementation of the control law, Larsen et al. studied a dynamic implementation of the S-controller suggested by Sepulchre and Kokotović. They showed the potential benefit of implementing the S-controller through a first-order lag: while the location of the closed-loop equilibrium achieved with the static control law was sensitive to poorly known parameters, the dynamic implementation resulted in a small limit cycle at a very desirable location, insensitive to parameter variations. In this paper, we investigate the more general case when the control is applied with a time delay. This can be seen as an extension of the model with a first-order lag. The delay can either be a result of system constraints or be deliberately implemented to achieve better system behavior. The resulting closed-loop system is a set of parameter-dependent delay differential equations. Numerical bifurcation analysis is used to study this model and investigate whether the positive results obtained for the first-order model persist, even for larger values of the delay.

Identification of the steering control behaviour of five test subjects following a randomly curving path in a driving simulator

The paper is concerned with the identification of theoretical preview steering controllers using data obtained from five test subjects in a fixed-base driving simulator. An understanding of human steering control behaviour is relevant to the design of autonomous and semi-autonomous vehicle controls. The driving task involved steering a linear vehicle along a randomly curving path. The theoretical steering controllers identified from the data were based on optimal linear preview control. A direct-identification method was used, and the steering controllers were identified so that the predicted steering angle matched as closely as possible the measured steering angle of the test subjects. It was found that identification of the driver's time delay and noise is necessary to avoid bias in identification of the controller parameters. Most subjects' steering behaviour was predicted well by a theoretical controller based on the lateral/yaw dynamics of the vehicle. There was some evidence that an inexperienced driver's steering action was better represented by a controller based on a simpler model of the vehicle dynamics, perhaps reflecting incomplete learning by the driver. Copyright © 2014 Inderscience Enterprises Ltd.

Retinal adaptation of visual processing time delays.

A significant proportion of the processing delays within the visual system are luminance dependent. Thus placing an attenuating filter over one eye causes a temporal delay between the eyes and thus an illusion of motion in depth for objects moving in the fronto-parallel plane, known as the Pulfrich effect. We have used this effect to study adaptation to such an interocular delay in two normal subjects wearing 75% attenuating neutral density filters over one eye. In two separate experimental periods both subjects showed about 60% adaptation over 9 days. Reciprocal effects were seen on removal of the filters. To isolate the site of adaptation we also measured the subjects' flicker fusion frequencies (FFFs) and contrast sensitivity functions (CSFs). Both subjects showed significant adaptation in their FFFs. An attempt to model the Pulfrich and FFF adaptation curves with a change in a single parameter in Kelly's [(1971) Journal of the Optical Society of America, 71, 537-546] retinal model was only partially successful. Although we have demonstrated adaptation in normal subjects to induced time delays in the visual system we postulate that this may at least partly represent retinal adaptation to the change in mean luminance.