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

Advances in model identification using the block-oriented exact solution technique in a predictive modeling framework

Obtaining an accurate model has always been a challenging objective in implementation of Model Predictive Control, especially for nonlinear processes. Part of this work here proposed a model building methodology for a complex block-oriented process, namely a Hammerstein-Wiener system in order to meet such a demand. It is a general system of the more simple structures which are known as Hammerstein and Wiener. This methodology uses sequential step test training data determined from an optimal experimental design and simultaneously estimates all the model coefficients under nonlinear least squares objective function. It is evaluated using four process examples and is compared with a recently proposed method in three of them. Even with less frequent sampling, the proposed method is demonstrated to have advantages in simplicity, the ability to model non-invertible systems, the ability to model multiple input and non-minimum phase processes, and accuracy.;This class of modeling method is also being applied to model normal operation plant data. The common problem seen in this type of dataset including high multi-collinearities of the inputs and low signal to noise ratios for the outputs inhibit modelers to acquire cause and effect relationship. The second part of the work here is to introduced this modeling approach that is capable of developing accurate cause and effect models. It is a special application of the Wiener block-oriented system and the unique and powerful attributes of this approach over existing techniques are demonstrated in a mathematically simulated processes and real processes

Networked Control System Design and Parameter Estimation

Networked control systems (NCSs) are a kind of distributed control systems in which the data between control components are exchanged via communication networks. Because of the attractive advantages of NCSs such as reduced system wiring, low weight, and ease of system diagnosis and maintenance, the research on NCSs has received much attention in recent years. The first part (Chapter 2 - Chapter 4) of the thesis is devoted to designing new controllers for NCSs by incorporating the network-induced delays. The thesis also conducts research on filtering of multirate systems and identification of Hammerstein systems in the second part (Chapter 5 - Chapter 6). Network-induced delays exist in both sensor-to-controller (S-C) and controller-to-actuator (C-A) links. A novel two-mode-dependent control scheme is proposed, in which the to-be-designed controller depends on both S-C and C-A delays. The resulting closed-loop system is a special jump linear system. Then, the conditions for stochastic stability are obtained in terms of a set of linear matrix inequalities (LMIs) with nonconvex constraints, which can be efficiently solved by a sequential LMI optimization algorithm. Further, the control synthesis problem for the NCSs is considered. The definitions of H₂ and H∞ norms for the special system are first proposed. Also, the plant uncertainties are considered in the design. Finally, the robust mixed H₂/H∞ control problem is solved under the framework of LMIs. To compensate for both S-C and C-A delays modeled by Markov chains, the generalized predictive control method is modified to choose certain predicted future control signal as the current control effort on the actuator node, whenever the control signal is delayed. Further, stability criteria in terms of LMIs are provided to check the system stability. The proposed method is also tested on an experimental hydraulic position control system. Multirate systems exist in many practical applications where different sampling rates co-exist in the same system. The l₂-l∞ filtering problem for multirate systems is considered in the thesis. By using the lifting technique, the system is first transformed to a linear time-invariant one, and then the filter design is formulated as an optimization problem which can be solved by using LMI techniques. Hammerstein model consists of a static nonlinear block followed in series by a linear dynamic system, which can find many applications in different areas. New switching sequences to handle the two-segment nonlinearities are proposed in this thesis. This leads to less parameters to be estimated and thus reduces the computational cost. Further, a stochastic gradient algorithm based on the idea of replacing the unmeasurable terms with their estimates is developed to identify the Hammerstein model with two-segment nonlinearities. Finally, several open problems are listed as the future research directions

Digital predistortion of RF amplifiers using baseband injection for mobile broadband communications

Radio frequency (RF) power amplifiers (PAs) represent the most challenging design parts of wireless transmitters. In order to be more energy efficient, PAs should operate in nonlinear region where they produce distortion that significantly degrades the quality of signal at transmitter’s output. With the aim of reducing this distortion and improve signal quality, digital predistortion (DPD) techniques are widely used. This work focuses on improving the performances of DPDs in modern, next-generation wireless transmitters. A new adaptive DPD based on an iterative injection approach is developed and experimentally verified using a 4G signal. The signal performances at transmitter output are notably improved, while the proposed DPD does not require large digital signal processing memory resources and computational complexity. Moreover, the injection-based DPD theory is extended to be applicable in concurrent dual-band wireless transmitters. A cross-modulation problem specific to concurrent dual-band transmitters is investigated in detail and novel DPD based on simultaneous injection of intermodulation and cross-modulation distortion products is proposed. In order to mitigate distortion compensation limit phenomena and memory effects in highly nonlinear RF PAs, this DPD is further extended and complete generalised DPD system for concurrent dual-band transmitters is developed. It is clearly proved in experiments that the proposed predistorter remarkably improves the in-band and out-of-band performances of both signals. Furthermore, it does not depend on frequency separation between frequency bands and has significantly lower complexity in comparison with previously reported concurrent dual-band DPDs

Black-Box Modelling of Nonlinear Audio Circuits

This Thesis details various black-box modelling techniques for nonlinear audio circuits. The aim of this work was to compare the different approaches and determine the current most accurate model. The models analysed were: Chebyshev polynomials, Hammerstein, polynomials of best fit and a parametric model. These implementations were compared based on their spectral accuracy and time-domain accuracy. From the analysis of these models, a new method is proposed. This proposed model restructures the determined most accurate black-box model by placing a nonlinearity between a high-pass and a low-pass filter. The filters emulate the linear response of the nonlinear circuit. These filters also have a reduced filter order in comparison to the linear response. The proposed method results in a model that performs close to the current best but does result in a massive reduction in computational time, up to 95% less time required and 99% fewer operations

Safe Experimentation Dynamics Algorithm for Identification of Cupping Suction Based on the Nonlinear Hammerstein Model

The use of cupping therapy for various health benefits has increased in popularity recently. Potential advantages of cupping therapy include pain reduction, increased circulation, relaxation, and skin health. The increased blood flow makes it easier to supply nutrients and oxygen to the tissues, promoting healing. Nevertheless, the effectiveness of this technique greatly depends on the negative pressure's ability to create the desired suction effect on the skin. This research paper suggests a method to detect the cupping suction model by employing the Hammerstein model and utilizing the Safe Experimentation Dynamics (SED) algorithm. The problem is that the cupping suction system experiences pressure leaks and is difficult to control. Although, stabilizing the suction pressure and developing an effective controller requires an accurate model. The research contribution lies in utilizing the SED algorithm to tune the parameters of the Hammerstein model specifically for the cupping suction system and figure out the real system with a continuous-time transfer function. The experimental data collected for cupping therapy exhibited nonlinearity attributed to the complex dynamics of the system, presenting challenges in developing a Hammerstein model. This work used a nonlinear model to study the cupping suction system. Input and output data were collected from the differential pressure sensor for 20 minutes, sampling every 0.1 seconds. The single-agent method SED has limited exploration capabilities for finding optimum value but excels in exploitation. To address this limitation, incorporating initial values leads to improved performance and a better match with the real experimental observations. Experimentation was conducted to find the best model parameters for the desired suction pressure. The therapy can be administered with greater precision and efficacy by accurately identifying the suction pressure. Overall, this research represents a promising development in cupping therapy. In particular, it has been demonstrated that the proposed nonlinear Hammerstein models improve accuracy by 84.34% through the tuning SED algorithm

State–of–the–art report on nonlinear representation of sources and channels

This report consists of two complementary parts, related to the modeling of two important sources of nonlinearities in a communications system. In the first part, an overview of important past work related to the estimation, compression and processing of sparse data through the use of nonlinear models is provided. In the second part, the current state of the art on the representation of wireless channels in the presence of nonlinearities is summarized. In addition to the characteristics of the nonlinear wireless fading channel, some information is also provided on recent approaches to the sparse representation of such channels

Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation

ULTRA-WIDEBAND NONLINEAR ECHO-CANCELLATION

Hybrid fiber coaxial (HFC) networks are used around the world to distribute cable television and broadband internet services to customers. These networks are governed by the Data-Over-Cable Service Interface Specification (DOCSIS) family of standards, with the most recent version at the time of this writing being DOCSIS 3.1. A frequency division duplex (FDD) spectrum is used in DOCSIS 3.1, where the upstream and downstream signals are separated in frequency to eliminate interference. A possible method to increase signal bandwidths is to use a full-duplex (FDX) spectrum, in which the US and DS signals use the same frequencies at the same time. A main challenge faced when implementing FDX in a DOCSIS node is eliminating the interference in the received US signal caused by the transmitted DS signal. One possible method for eliminating the interference is utilizing an echo-canceling algorithm, which predicts the self-interference (SI) based on the known DS signal and cancels it from the received US signal. Although echo-cancellation algorithms exist for fundamentally similar applications, the DOCSIS FDX case is more complicated for two main reasons. First, the DOCSIS node uses a nonlinear power amplifier to amplify the DS signal. Second, the DS signal is an ultra-wideband signal spanning a frequency range of up to 1.2 GHz. Most of the amplifier modeling techniques discussed in the literature were designed for narrowband wireless signals and will have limited performance when used with ultra-wideband signals. This thesis develops an algorithm to characterize the power amplifier and to predict the harmonics it generates for a given DS signal. These predicted harmonics can be used to cancel the SI signal in a full duplex DOCSIS system. The algorithm, which is referred to as the ultra-wideband memory polynomial (UWB-MP) model, is based on the well-known memory polynomial model with adaptations which allow the model to predict harmonics for ultra-wideband signals. Since a direct implementation of the UWB-MP model in an FPGA would result in very high resource usage, system architecture recommendations are provided. Our proposed implementation of the model compensates for harmonics up to and including the 3rd order, which has a power spectrum extending above 3600 MHz. Using the techniques discussed in this thesis, it is shown that a sampling rate of 4 GHz allows for cancellation of the SI signal while providing a reasonable balance between performance and resource usage. Matlab simulations of a DOCSIS node with various parameters and PA simulation models were conducted. The simulations showed that over 75 dB of cancellation of the SI signal is possible in an idealized hardware setup. It is also demonstrated that AWGN injected into the received signal does not reduce the ability of the model to estimate the PA harmonics, although the noise itself cannot be canceled. Further simulations showed that the UWB-MP model could cancel harmonics whose power is much higher than that specified in DOCSIS. Although the UWB-MP model was designed with memory polynomial type PAs in mind, simulation results show that significant cancellation is possible with PAs that are represented by Wiener models as well. Based on the simulation results, we recommend using a filter of length 20 coefficients for each harmonic in the UWB-MP model, and 60 iterations with 500 samples for estimating the coefficients with the least squares method