Delay compensated control of the Stefan problem and robustness to delay mismatch

This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.     

Low-Power VLSI Implementation of the Inner Receiver for OFDM-Based WLAN Systems

In this paper, we propose low-power designs for the synchronizer and channel estimator units of the Inner Receiver in wireless local area network systems. The objective of the work is the optimization, with respect to power, area, and latency, of both the signal processing algorithms themselves and their implementation. Novel circuit design strategies have been employed to realize optimal hardware and power efficient architectures for the fast Fourier transform, arc tangent computation unit, numerically controlled oscillator, and the decimation filters. The use of multiple clock domains and clock gating reduces the power consumption further. These blocks have been integrated into an experimental digital baseband processor for the IEEE 802.11a standard implemented in the 0.25mum- 5-metal layer BiCMOS technology from Institute for High Performance Microelectronics.     

Adaptive output-feedback stabilization of non-local hyperbolic PDEs

We address the problem of adaptive output-feedback stabilization of general first-order hyperbolic partial integro-differential equations (PIDE). Such systems are also referred to as PDEs with non-local (in space) terms. We apply control at one boundary, take measurements on the other boundary, and allow the system’s functional coefficients to be unknown. To deal with the absence of both full-state measurement and parameter knowledge, we introduce a pre-transformation (which happens to be based on backstepping) of the system into an observer canonical form. In that form, the problem of adaptive observer design becomes tractable. Both the parameter estimator and the control law employ only the input and output signals (and their histories over one unit of time). Prior to presenting the adaptive design, we present the non-adaptive/baseline controller, which is novel in its own right and facilitates the understanding of the more complex, adaptive system. The parameter estimator is of the gradient type, based on a parametric model in the form of an integral equation relating delayed values of the input and output. For the closed-loop system we establish boundedness of all signals, pointwise in space and time, and convergence of the PDE state to zero pointwise in space. We illustrate our result with a simulation.     

Stochastic source seeking for nonholonomic unicycle

We apply the recently introduced method of stochastic extremum seeking to navigate a nonholonomic unicycle towards the maximum of an unknown, spatially distributed signal field, using only the measurement of the signal at the vehicle’s location but without the measurement of the vehicle’s position. Keeping the forward velocity constant and controlling only the angular velocity, we design a stochastic source seeking control law which employs excitation based on filtered white noise, rather than sinusoidal perturbations used in the existing work. We study stability with the help of stochastic averaging theorems that we recently developed for general nonlinear continuous-time systems with stochastic perturbations. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source. We characterize the convergence speed explicitly and provide design guidelines for maximizing it, as well as for minimizing the residual set near the source. We present a detailed simulation study, including a study of the effect of saturation on the steering input.     

Functionally testable path delay faults on a microprocessor

The impact of delay defects on these functionally untestable paths on overall circuit performance involves identification of such paths determining the achievable path delay fault coverage and reducing the subsequent test generation effort. The experimental results for two microprocessors (Parwan and DLX) indicate that a significant percentage of structurally testable paths are functionally untestable     

Influence of elastic and thermal mismatch on the local crack-driving force in brittle composites

An expression is derived for the change of localK ₁ value of a crackfront near circular and spherical inclusions with elastic moduli and thermal expansion coefficient different from those of the matrix. The derivation is based on the concept of an image stress which is imposed on the crack, to illustrate the interaction between elastic and thermal stress concentrations developed around inclusions in a composite material and the crack-tip stress field.     

Useful nonlinearities and global stabilization of bifurcations in amodel of jet engine surge and stall

Compressor stall and surge are complex nonlinear instabilities that reduce the performance and can cause failure of aircraft engines. We design a feedback controller that globally stabilizes a broad range of possible equilibria in a nonlinear compressor model. With a novel backstepping design we retain the system's useful nonlinearities which would be cancelled in a feedback linearizing design. The design control law is simple and, moreover, it is optimal with respect to a meaningful nonquadratic cost functional. As in a previous bifurcation-theoretic design, we change the character of the bifurcation at the stall inception point from subcritical to supercritical. However, since we approach the bifurcation control using Lyapunov tools, our controller achieves not only local but also global stability. The controller requires minimal modeling information and simpler sensing (rotating stall is stabilized without measuring its amplitude)     

Robustness of the tuning functions adaptive backstepping design forlinear systems

We study robustness of the adaptive backstepping design with tuning functions for linear systems. Under assumptions on unmodeled dynamics and disturbances equal to those for certainty equivalence schemes, we address an adaptive scheme not based on the certainty equivalence principle. In the process of redesign for robustness we employ only leakage in the estimator; we do not employ normalization, neither static nor dynamic. A fundamental difference between the tuning functions design and the certainty equivalence designs is that the controller in the former is inherently nonlinear, while in the latter it is nonlinear only in the parameter estimate. As a result, achievable robustness results for the tuning functions scheme are not global but regional, with a region of attraction inversely proportional to the “size” of the unmodeled dynamics. The tracking error is proportional to the size of the uncertainties     

Feedback linearizability and explicit integrator forwarding controllers for classes of feedforward systems

We identify a class of feedforward nonlinear systems that are linearizable by a coordinate change. Then we develop explicit expressions for the Lyapunov-based integrator forwarding recursive procedure of Sepulchre, Jankovic, and Kokotovic, which has its roots in a coordinate transformation proposed by Mazenc and Praly. The explicit expressions that we develop allow us to also find closed-form control laws for several classes of systems that are not feedback linearizable, including some that are in the feedforward form and others that are in what we refer to as the "block-feedforward" form. Performance advantages of Lyapunov-based forwarding controllers over nested saturation controllers have been well illustrated in the literature on examples. The analytical expressions for the Lyapunov functions and the control laws allow us to give quantitative performance bounds.     

Chemical sputtering of deuterated carbon surfaces at various surface temperatures

The chemical sputtering of deuterated amorphous carbon (a-C:D) surfaces irradiated by 1-50 eV deuterium atoms at surface temperatures between 300 and 1000 K was studied using classical molecular dynamics. A quasi-stationary state was reached by cumulative bombardment for each energy and temperature. Results were compared with available experimental data and previous modeling results and the applicability of molecular dynamics for thermally generated processes was discussed. An attempt is made to correct the absence of the thermally stimulated desorption/degassing of hydrogen from the MD simulations, which evolve at the longer time scales.