Individual Input Channel Research Articles

ISS of predictor feedback for multi-input affine nonlinear systems with distinct input delays

We develop a predictor feedback control scheme for multi-input affine nonlinear systems with distinct input delays in each individual input channel and additive disturbances. The input-to-state stable control Lyapunov function (ISS-CLF) is used to design control laws for the delay-free affine nonlinear systems. Then, a predictor-feedback controller is constructed for this class of nonlinear systems with input delays. We establish input-to-state stability with respect to additive plant disturbances, as well as we show that the control law derives gain margin guarantees. Our proofs are based on the infinite-dimensional backstepping transformation and the construction of a Lyapunov functional. The developed method is applied to the control of vehicular traffic flow at distant bottlenecks.

Multivariable Extremum Seeking for PDE Dynamic Systems

In this article, we address the design and analysis of multivariable Newton-based extremum seeking (ES) for static locally quadratic maps subject to actuation dynamics governed by diffusion partial differential equations (PDEs). Multi-input systems with distinct diffusion coefficients in each individual input channel are dealt with. The phase compensation of the dither signals is handled as a trajectory generation problem and the inclusion of a multivariable diffusion feedback controller with a perturbation-based (averaging-based) estimate of the Hessian's inverse allow to obtain local exponential convergence results to a small neighborhood of the optimal point. The stability analysis is carried out using backstepping transformation and averaging in infinite dimensions, capturing the infinite-dimensional state due the diffusion PDEs. In addition, the generalization of the results for different classes of parabolic (reaction-advection-diffusion) PDEs, wave equations and/or first-order hyperbolic (transport-dominated) PDEs is also discussed. As for ordinary differential equations case, the proposed Newton approach removes the dependence of the algorithm's convergence rate on the unknown Hessian of the nonlinear map to be optimized, being user-assignable unlike the gradient algorithm. A numerical example illustrates the performance of our multivariable ES for compensating PDE-based systems.

Identification of MISO systems in Minimal Realization Form

The paper is concerned with identifying transfer functions of individual input channels in minimal realization form of a Multi-Input Single Output (MISO) from the input-output data corrupted by the error in all the variables. Such a framework is commonly referred to as error-in-variables (EIV). A common approach in the existing methods for identification of MISO systems is to estimate a non-minimal order transfer function under a subset of simplistic assumptions like homoskedastic error variances, known order, and delay. In this work, we deal with the challenging problem of identifying order, delay in each input of minimal realization form separately while estimating the transfer functions. We also estimate the heteroskedastic noise variances in each of the multiple inputs and output variables. An automated approach for the identification of MISO systems of minimal realization form in the EIV framework is proposed. Numerical case studies are presented to illustrate the efficacy of the proposed algorithm in identifying the transfer function along with the order, delay, and noise variances.

PDE Boundary Control of Multi-Input LTI Systems With Distinct and Uncertain Input Delays

Taking advantage of the concept of a transport partial differential equation (PDE) representation of the delayed input, we propose a predictor-feedback control for the stabilization of multi-input linear time-invariant (LTI) systems with distinct input delays. Different from recently published results about predictor feedbacks for multi-input time delay systems that require a perfect knowledge of the length of delays, the LTI plants taken into account in this paper have the uncertain and distinct time delay in each individual input channel. To deal with the problem of the unknown multi-input delays and the consequently unmeasurable distributed input, an adaptive PDE boundary control scheme including an estimation of the unmeasured transport PDE state and an online identification of the unknown delay is developed. The conventional backstepping transformation for the known delay case is also replaced by a unity-rescaled backstepping transformation for the case of delay adaptation. With Lyapunov-based analysis, we show local stability of the delay-adaptive prediction-based closed-loop systems.

Extremum Seeking for Static Maps With Delays

In this paper, we address the design and analysis of multi-variable extremum seeking for static maps subject to arbitrarily long time delays. Both Gradient and Newton-based methods are considered. Multi-input systems with different time delays in each individual input channel as well as output delays are dealt with. The phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation-based (averaging-based) estimate of the Hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point, even in the presence of delays. The stability analysis is carried out using backstepping transformation and averaging in infinite dimensions, capturing the infinite-dimensional state due the time delay. In particular, a new backstepping-like transformation is introduced to design the predictor for the Gradient-based extremum seeking scheme with multiple and distinct input delays. The proposed Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the nonlinear map to be optimized, being user-assignable as in the literature free of delays. A source seeking example illustrates the performance of the proposed delay-compensated extremum seeking schemes.

Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different time instants, the key design challenge, which we resolve, is the construction of the predictors of the plant's state over distinct prediction horizons such that the corresponding input delays are compensated. Global asymptotic stability of the closed-loop system is established by constructing a Lyapunov functional.

Exact predictor feedbacks for multi-input LTI systems with distinct input delays

This paper proposes a predictor-based state feedback controller for multi-input linear time-invariant (LTI) systems with different time delays in each individual input channel. The controller is derived based on the backstepping method. Since the conventional backstepping transformation is not applicable to the systems due to the differences among delays, a modified transformation is introduced. This transformation enables us to design an exponentially stabilizing controller under which the plant behaves as if the delays were absent after a finite time interval. As a dual of the controller design, we also present the observer design for multi-output LTI systems with distinct sensor delays. A numerical simulation confirms the performance of the proposed controller.

Real time input subset selection for linear time-variant MIMO systems

In this paper we propose an approach for multi-input multi-output (MIMO) system identification when the statistical relationship between input and output varies in input space as well as in time; i.e. nonstationary in space and time. An on-line variable selection algorithm, which has been recently developed for selecting a subset of input variables in real time by modifying least angle regression (LAR) with recursive estimators, is extensively applied to the linear time-variant MIMO systems. In our approach, a subset of input channels relevant with output is selected at every time instance based on the correlation between the filtering outcome of individual input channels and desired output. The on-line variable selection algorithm performs channel selection with weights using this real-time correlation. The proposed model is compared with a typical linear model in which only the least mean squares (LMS) is used to update system parameters. Tracking performances of these two models are demonstrated in a computer simulation and in a real-world application for tracking a linear relationship between neural firing rates of a primate and synchronously recorded hand kinematics. In both cases, our model demonstrates superior tracking performance.

Development of front end electronics for M-MSGC using individual-readout ASIC with resistive strip output

A multi-grid-type microstrip gas chamber (M-MSGC) is being developed for the new spallation neutron source in Japan. The objective of this study is to provide a new position readout electronics for two-dimensional M-MSGC which can reduce the number of interconnections through a gas vessel by using a new encoding readout scheme based on ASIC technology. In order to test an ASIC based individual readout method, an ASIC chip, which has typically 16 individual input channels, has been designed and fabricated using a ROHM 0.35µ;m CMOS process and the chip was connected to a developed encoding circuit. The main results of the performance test indicated that the front-end electronics was able to encode 1500 pixels of the input position with 4.4% of position non-linearity. The results of this work confirm that the developed circuit would be appropriate for the front-end electronics of He-3 two-dimensional M-MSGC.

Modular PC-based data acquisition and processing system for biological signals

The data acquisition system described here is designed for biomedical research and permits the recording of up to eight biological signals simultaneously. A personal computer using the Windows 95 operating system is employed for data monitoring, data processing and analysis during experiments. The system has been designed for reliability, economy, flexibility and ease of handling, with the aim of achieving universal application. To avoid interface incompatibility, problems with transfer protocols and the data formats of commercially available products, analog signals are used for further processing. The individual input channels are electrically isolated from one another and the PC to avoid ground loops, and for reasons of safety. An isolated voltage supply is available for pre-amplifiers and bridges. A bandwidth of 0-5 kHz and the maximum sampling rate of 12.5 kHz suffice to pick up higher frequency signals such as EMG and ENG. The modular software and hardware concepts permit the use of almost any desktop or laptop PC as a central processing unit. The PC handless documentation, data acquisition, data analysis and the preparation of publications. If needed, further analytical functions can be added in modular form. Finally, the option of saving data in the ASCII format permits processing of results with such standard software packages as Excel, Access, Matlab and Origin.

An ultrafast photonic ATM switch based on bit-interleave multiplexing

An optical ATM switch is proposed in which cells from individual input channels are time-division multiplexed in a bit-interleave manner. This switch can easily handle multicast switching because it is based on a broadcast-and-select network. Compared to an alternative switch that uses a cell-interleave time-division multiplexing scheme, the proposed optical switch has a much simpler structure. It does not need a cell compressor at each input and a cell expander at each output, which greatly reduces hardware complexity. Feasibility analyzes showed that a 64/spl times/64 photonic ATM switch with 2.5 Gb/s input/output is possible using the proposed technology. In an experimental demonstration, 4 b cells were selected from a 55 Gb/s bit-interleave multiplexed cell stream by using a new nonlinear optical fiber switch. With its high switch throughput, our switch is a strong candidate for future large-capacity optical switching nodes.

Optical bit-interleave multiplexing ATM switch

A new optical ATM switch is proposed in which cells from individual input channels are time multiplexed by bit-interleaving. Compared to an earlier counterpart that used a cell-interleave time multiplexing scheme, the proposed switch has a much simpler structure, which significantly reduces hardware complexity. A basic demultiplexing experiment is carried out as a test.

Identification of Parameters and Time Delays of Continuous Systems using the Genetic Algorithm

This report proposes a novel method of identification of continuous time-delay systems from sampled inputoutput data. By the aid of a digital pre-filter, an approximated discrete-time estimation model is first derived, in which the system parameters remain in their original form and the time delay need not be an integral multiple of the sampling period. Then an identification method combining the common linear least squares (LS) method or the instrumental variable (IV) method with the genetic algorithm (GA) is proposed. That is, the time-delay is selected by the GA, and the system parameters are estimated by the LS or IV method. Furthermore, the proposed method is extended to the case of multi-input multi-output(MIMO) systems where the time-delays in the individual input channels may differ each other. Simulation results show that our method yields accurate estimates even in the presence of high measurement noises.

High-rate CAMAC acquisition system

The High Energy Resolution Ball (HERB) consists of 21 Bismuth-germanate shielded germanium detectors, clustered in three rings. In the center of the cluster is a 40 element bismuth-germanate ball which functions as a sum spectrometer and a multiplicity filter. The purpose of the system is to measure the energy, multiplicity, and correlations of gamma rays emitted from a target located in the center of the ball. This paper describes the data acquisition hardware and software which was developed to support this apparatus. The high data rates generated are handled by two levels of FIFO buffering in CAMAC hardware. Also of interest is the method of calibrating the individual analog input channels. The software obtains calibration information from the incoming experimental data and sets up a special CAMAC module which dynamically adjusts the gain and offset of each input channel.