The problems of identification, analysis and optimal control have been recently studied via orthogonal functions. The particular orthogonal functions used up to now are the Walsh, the block-pulse and the Laguerre functions. In this paper, the Chebyshev functions are introduced and solutions for the aforementioned problems are established. The algorithms proposed are analogous to those already derived for the Walsh, block-pulse and Laguerre functions. The Chebyshev series approach presented here appears to have certain advantages over other orthogonal series, and they may therefore be more suitable for the study of the problems of identification, analysis and optimal control.

Chebyshev series approach to system identification, analysis and optimal control

This paper describes a fault tolerant steer-by-wire road wheel control system. With dual motor, dual microcontroller architecture this system has the capability to tolerate single point failure without degrading the control system performance. The arbitration bus, mechanical arrangement of motors, and the developed control algorithm allow the system to reconfigure itself automatically in the event of a single point fault, and assure a smooth reconfiguration procedure. The experimental result illustrates the effectiveness of the proposed system.

http://ieeexplore.ieee.org/iel5/9861/31519/01470199.pdf

Fault tolerant steer-by-wire road wheel control system

A method is presented for identifying the transfer function matrix of a continuous-time multivariate system with unknown initial conditions from sampled data of input-output measurements. Using the so-called linear integral filter, an operation of numerical integration for handling time derivatives of measurements, leads to an identification model without involving the unknown initial conditions, and thus they do not require estimation together with the system parameters. Both a theoretical analysis and simulation study show that the least squares estimates are asymptotically biased even when the system outputs are corrupted by white noise. An instrumental variable method, where instrumental variables are composed of combinations of input signals, is proposed to give consistent estimates of system parameters for open-loop operation, and it is also thoroughly evaluated by Monte Carlo simulation analysis.

Recursive identification of transfer function matrix in continuous systems via linear integral filter

Direct methods for recursive identification of continuous systems from sampled input–output data using digital low–pass filters are discussed. The digital low–pass filters are introduced to avoid direct approximations of system signal derivatives from sampled data. Using a pre–designed digital low–pass filter, an approximated discrete–time estimation model is constructed easily. Thus the system parameters can be identified directly by recursive identification algorithms. Numerical results, show that the parameter estimates are not so sensitive to the pass-band of the filter, and if the filter is designed so that its pass-band matches that of the system closely and thus the noise effects are sufficiently reduced, accurate estimates can be obtained by recursive identification algorithms. Two classes of filters (FIR digital filter and IIR digital filter) are considered. It is shown that some other methods can be unified to be either the IIR or the FIR filtering approach.

Identification of continuous systems using digital low-pass filters

A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of ∫ 0 t s(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method.

Parameter identification of a class of time-varying systems via orthogonal shifted legendre polynomials

Using the elegant operational properties of block-pulse functions, a new recursive algorithm for identifying single-input-single-output (SISO) dynamic systems on-line is developed. Compared with the Walsh function approach, the proposed method is much simpler and more convenient for use in computers. Some examples are presented to illustrate the use of this method

Ning-Show Hsu

Papers

Single-input-single-output system identification via block-pulse functions