Nonlinear system modeling based on constrained Volterra series estimates

A simple nonlinear system modeling algorithm designed to work with limited \emph{a priori }knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an $l_{q}$-constrained least squares algorithm with $q\geq 1$. If the system $m\left( \cdot \right)$ is a continuous and bounded map with a finite memory no longer than some known $\tau$, then (for a $D$ parameter model and for a number of measurements $N$) the difference between the resulting model of the system and the best possible theoretical one is guaranteed to be of order $\sqrt{N^{-1}\ln D}$, even for $D\geq N$. The performance of models obtained for $q=1,1.5$ and $2$ is tested on the Wiener-Hammerstein benchmark system. The results suggest that the models obtained for $q>1$ are better suited to characterize the nature of the system, while the sparse solutions obtained for $q=1$ yield smaller error values in terms of input-output behavior

Maternity leave

A numerous off-days which a woman is legally approved to be absent from work in the weeks prenatal and postnatal recovery phase after giving birth defines maternity leave. It is stated that at least 60 consecutive days of paid maternity leave were entitled to all female workers in Malaysia if they have worked at least 90 days with their current employers in four months leading up to their confinement period, except for exempted categories (Employment Act 1955) During the maternity leave, female workers are entitled to be provided with all relevant contractual benefits and paid with full salary as if they are in an active employment excluding the benefits that are tied to active work. The right to resume working upon their return from maternity leave is also protected

NONLINEAR IDENTIFICATION AND CONTROL: A PRACTICAL SOLUTION AND ITS APPLICATION

It is well known that typical welding processes such as laser welding are nonlinear although mostly they are treated as linear system. For the purpose of automatic control, Identification of nonlinear system, especially welding processes is a necessary and fundamental problem. The purpose of this research is to develop a simple and practical identification and control for welding processes. Many investigations have shown the possibility to represent physical processes by nonlinear models, such as Hammerstein structure, consisting of a nonlinearity and linear dynamics in series with each other. Motivated by the fact that typical welding processes do not have non-zeroes, a novel two-step nonlinear Hammerstein identification method is proposed for laser welding processes. The method can be realized both in continuous and discrete case. To study the relation among parameters influencing laser processing, a standard diode laser processing system is built as system prototype. Based on experimental study, a SISO and 2ISO nonlinear Hammerstein model structure are developed to approximate the diode laser welding process. Specific persistent excitation signals such as PRTS (Pseudo-random-ternary-series) to Step signal are used for identification. The model takes welding speed as input and the top surface molten weld pool width as output. A vision based sensor implemented with a Pulse-controlled-CCD camera is proposed and applied to acquire the images and the geometric data of the weld pool. The estimated model is then verified by comparing the simulation and experimental measurement. The verification shows that the model is reasonably correct and can be use to model the nonlinear process for further study. The two-step nonlinear identification method is proved valid and applicable to traditional welding processes and similar manufacturing processes. Based on the identified model, nonlinear control algorithms are also studied. Algorithms include simple linearization and backstepping based robust adaptive control algorithm are proposed and simulated

Parameter Estimation of Switched Hammerstein Systems

This paper deals with the parameter estimation problem of the Single-Input-Single-Output (SISO) switched Hammerstein system. Suppose that the switching law is arbitrary but can be observed online. All subsystems are parameterized and the Recursive Least Squares (RLS) algorithm is applied to estimate their parameters. To overcome the difficulty caused by coupling of data from different subsystems, the concept "intrinsic switch" is introduced. Two cases are considered: i) The input is taken to be a sequence of independent identically distributed (i.i.d.) random variables when identification is the only purpose; ii) A diminishingly excited signal is superimposed on the control when the adaptive control law is given. The strong consistency of the estimates in both cases is established and a simulation example is given to verify the theoretical analysis.Comment: 16 pages, 3 figures; Accepted for publication by Acta Mathematicae Applicatae Sinica (http://link.springer.com/journal/10255