Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique

By extending the least squares-based iterative (LSI) method, this paper presents a decomposition-based LSI (D-LSI) algorithm for identifying linear-in-parameters systems and an interval-varying D-LSI algorithm for handling the identification problems of missing-data systems. The basic idea is to apply the hierarchical identification principle to decompose the original system into two fictitious sub-systems and then to derive new iterative algorithms to estimate the parameters of each sub-system. Compared with the LSI algorithm and the interval-varying LSI algorithm, the decomposition-based iterative algorithms have less computational load. The numerical simulation results demonstrate that the proposed algorithms work quite well

Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Aerodynamic parameter estimation via Fourier modulating function techniques

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models

Malliprediktiivinen säädin Tennessee Eastman prosessille

This thesis aims to design a multivariable Model Predictive Control (MPC) scheme for a complex industrial process. The focus of the thesis is on the implementation and testing of a linear MPC control strategy combined with fault detection and diagnosis methods. The studied control methodology is based on a linear time invariant state-space model and the quadratic programming optimization procedure. The control scheme is realized as a supervisory one, where the MPC is used to calculate the optimal set point trajectories for the lower level PI controllers, thus aiming to decrease the fluctuations in the end product flows. The Tennessee Eastman (TE) process is used as the testing environment. The TE process is a benchmark based on a real process modified for testing. It has five units, four reactants, an inert, two products and a byproduct. The control objective is to maintain the production rate and the product quality at the desired level. To achieve this, the MPC implemented in this thesis gives setpoints to three stabilizing PI control loops around the reactor and the product stripper. The performance of the designed control systems is evaluated by inducing process disturbances, setpoint changes, and faults for two operational regimes. The obtained results show the efficiency of the adopted approach in handling disturbances and flexibility in control of different operational regimes without the need of retuning. To suppress the effects caused by faults, an additional level that provides fault detection and controller reconfiguration should be developed as further research.Tämän diplomityön tavoite on suunnitella monimuuttujainen-malliprediktiivinen säädin (MPC) teolliselle prosessille. Diplomityö keskittyy toteuttamaan ja testaamaan lineaarisen MPC strategian, joka yhdistettynä vikojen havainnointiin ja tunnistukseen sekä uudelleen konfigurointiin voidaan laajentaa vikasietoiseksi. Tutkittu säätöstrategia perustuu lineaariseen ajan suhteen muuttumattomaan tilataso-malliin ja neliöllisen ohjelmoinnin optimointimenetelmään. Säätö on toteutettu nk. ylemmän tason järjestelmänä, eli MPC:tä käytetään laskemaan optimaaliset asetusarvot alemman säätötason PI säätimille, tavoitteena vähentää vaihtelua lopputuotteen virroissa. Tennessee Eastman (TE) prosessia käytetään testiympäristönä. TE on testiprosessi, joka perustuu todelliseen teollisuuden prosessiin ja jota on muokattu testauskäyttöön sopivaksi. Prosessissa on viisi yksikköä, neljä lähtöainetta, inertti, kaksi tuotetta ja yksi sivutuote. Säätötavoite on ylläpitää haluttu taso tuotannon määrässä ja laadussa. Tämän saavuttamiseksi tässä diplomityössä toteutettu MPC antaa asetusarvoja kolmelle stabiloivalle PI-säätimelle reaktorin ja stripperin hallinnassa. Säätösysteemin suorituskykyä arvioitiin aiheuttamalla prosessiin häiriöitä, asetusarvon muutoksia ja vikoja eri operatiivisissa olosuhteissa. Saavutetut tulokset osoittavat valitun menetelmän tehokkuuden häiriöiden käsittelyyn ja joustavaan säätöön eri olosuhteissa. Tutkimuksen jatkokehityksenä vikojen vaikutuksen vaimentamiseksi säätöön tulisi lisätä taso, joka havaitsee viat ja uudelleen konfiguroi säätimen sen mukaisesti

Robust identification and controller design for delay processes

Ph.DDOCTOR OF PHILOSOPH

Development of adaptive control methodologies and algorithms for nonlinear dynamic systems based on u-control framework

Inspired by the U-model based control system design (or called U-control system design), this study is mainly divided into three parts. The first one is a U-model based control system for unstable non-minimum phase system. Pulling theorems are proposed to apply zeros pulling filters and poles pulling filters to pass the unstable non-minimum phase characteristics of the plant model/system. The zeros pulling filters and poles pulling filters derive from a customised desired minimum phase plant model. The remaining controller design can be any classic control systems or U-model based control system. The difference between classic control systems and U-model based control system for unstable non-minimum phase will be shown in the case studies.Secondly, the U-model framework is proposed to integrate the direct model reference adaptive control with MIT normalised rules for nonlinear dynamic systems. The U-model based direct model reference adaptive control is defined as an enhanced direct model reference adaptive control expanding the application range from linear system to nonlinear system. The estimated parameter of the nonlinear dynamic system will be placement as the estimated gain of a customised linear virtual plant model with MIT normalised rules. The customised linear virtual plant model is the same form as the reference model. Moreover, the U-model framework is design for the nonlinear dynamic system within the root inversion.Thirdly, similar to the structure of the U-model based direct model reference adaptive control with MIT normalised rules, the U-model based direct model reference adaptive control with Lyapunov algorithms proposes a linear virtual plant model as well, estimated and adapted the particular parameters as the estimated gain which of the nonlinear plant model by Lyapunov algorithms. The root inversion such as Newton-Ralphson algorithm provides the simply and concise method to obtain the inversion of the nonlinear system without the estimated gain. The proposed U-model based direct control system design approach is applied to develop the controller for a nonlinear system to implement the linear adaptive control. The computational experiments are presented to validate the effectiveness and efficiency of the proposed U-model based direct model reference adaptive control approach and stabilise with satisfied performance as applying for the linear plant model

Multivariate Statistical Process Monitoring and Control

Application of statistical methods in monitoring and control of industrially significant processes are generally known as statistical process control (SPC). Since most of the modern day industrial processes are multivariate in nature, multivariate statistical process control (MVSPC), supplanted univariate SPC techniques. MVSPC techniques are not only significant for scholastic pursuit; it has been addressing industrial problems in recent past. . Monitoring and controlling a chemical process is a challenging task because of their multivariate, highly correlated and non-linear nature. Present work based on successful application of chemometric techniques in implementing machine learning algorithms. Two such chemometric techniques; principal component analysis (PCA) & partial least squares (PLS) were extensively adapted in this work for process identification, monitoring & Control. PCA, an unsupervised technique can extract the essential features from a data set by reducing its dimensionality without compromising any valuable information of it. PLS finds the latent variables from the measured data by capturing the largest variance in the data and achieves the maximum correlation between the predictor and response variables even if it is extended to time series data. In the present work, new methodologies; based on clustering time series data and moving window based pattern matching have been proposed for detection of faulty conditions as well as differentiating among various normal operating conditions of Biochemical reactor, Drum-boiler, continuous stirred tank with cooling jacket and the prestigious Tennessee Eastman challenge processes. Both the techniques emancipated encouraging efficiencies in their performances. The physics of data based model identification through PLS, and NNPLS, their advantages over other time series models like ARX, ARMAX, ARMA, were addressed in the present dissertation. For multivariable processes, the PLS based controllers offered the opportunity to be designed as a series of decoupled SISO controllers. For controlling non-linear complex processes neural network based PLS (NNPLS) controllers were proposed. Neural network; a supervised category of data based modeling technique was used for identification of process dynamics. Neural nets trained with inverse dynamics of the process or direct inverse neural networks (DINN) acted as controllers. Latent variable based DINNS’ embedded in PLS framework termed as NNPLS controllers. (2×2), (3×3), and (4×4) Distillation processes were taken up to implement the proposed control strategy followed by the evaluation of their closed loop performances. The subject plant wide control deals with the inter unit interactions in a plant by the proper selection of manipulated and measured variables, selection of proper control strategies. Model based Direct synthesis and DINN controllers were incorporated for controlling brix concentrations in a multiple effect evaporation process plant and their performances were compared both in servo and regulator mode

Dynamic Model Identification and Trajectory Correction for Virtual Process Planning in Multi-Axis Machine Tools

In today’s industry, the capability to effectively reduce production time and cost gives a manufacturer a vital advantage against its competitors. Specifically, in the machining industry, the ability to simulate the dynamic performance of machine tools, and the physics of cutting processes, is critical to taking corrective actions, achieving process and productivity improvements, thereby enhancing competitiveness. In this context, being able to estimate mathematical models which describe the dynamic response of machine tools to commanded tool trajectories and external disturbance forces plays a key role in establishing virtual and intelligent manufacturing capability. These models can also be used in virtual simulations for process improvement, such as compensating for dynamic positioning errors by making small corrections to the commanded trajectory. This, in turn, can facilitate further productivity improvement and part quality in multi-axis manufacturing operations, such as machining. This thesis presents new methods for identifying the positioning response and friction characteristics of machine tool servo drives in a nonintrusive manner, and an approach for enhancing dynamic positioning accuracy through commanded trajectory correction via Iterative Learning Control (ILC). As the first contribution, the linear transfer functions correlating the positioning response to the commanded trajectory and friction disturbance inputs are identified using a new pole search method in conjunction with least squares (LS) projection. It is validated that this approach can work with in-process collected data, and demonstrates superior convergence and numerical characteristics, and model prediction accuracy, compared to an earlier ‘rapid identification’ approach based on the application of classical Least Squares for the full model. Effectiveness of the new method is demonstrated in simulations, and in experimental case studies for planar motion on two different machine tools, a gear grinding machine and a 5-axis machining center. Compared to the earlier approach, which could predict servo errors with 10-68% closeness, the new method improves the prediction accuracy to 0.5-2%. In the simulation of feed drives used in multi-axis machines, high fidelity prediction of the nonlinear stick-slip friction plays an important role. Specifically, time-dependent (i.e., dynamic) friction models help to improve the accuracy of virtual predictions. While many elaborate models have been proposed for this purpose, such as the generalized Maxwell-slip (GMS) model, their parameters can be numerous and difficult to identify from limited field data. In this thesis, as the second contribution, a new and highly efficient method of parameterizing the pre-sliding (hysteretic) portion of the GMS friction model is presented. This approach drastically reduces the number of unknown variables to identify, by estimating only the affective breakaway force, breakaway displacement, and ‘shape factor’ describing the shape of the pre-sliding virgin curve. Reduction in the number of unknowns enables this ‘reduced parameter’ GMS model to be identified much more easily from in-process data, compared to the fully parameterized GMS model, and the time-dependent friction dynamics can still be simulated accurately. Having improved the positioning response transfer function estimation and friction modeling, as the third contribution of this thesis, these two elements are combined together in a 3-step process. First, the servo response is estimated considering simplified Coulomb friction dynamics. Then, the friction model is replaced and identified as a reduced parameter GMS model. In the third step, the transfer function poles and zeros, and the reduced parameter GMS model, are concurrently optimized to replicate the observed experimental response with even greater fidelity. This improvement has been quantified as 12-44% in RMS and 28-54% in MAX values. This approach is successful in servo systems with predominantly rigid body behavior. However, its extension to a servo system with vibratory dynamics did not produce an immediately observed improvement. This is attributed to the dominance of vibrations in response to the commanded trajectory, and further investigation is recommended for future research. Having an accurate model of a multi-axis machine’s feed drive response allows for the dynamic positioning errors, which can lead to workpiece inaccuracy or defects, to be predicted and corrected ahead of time. For this purpose, ILC has been investigated. It is shown that through ILC, 1-2 orders of magnitude reduction in the servo errors is possible. While ILC is already available in certain commercial CNC systems, its training cycle (which is performed during the operation of the machine tool) can lead to part defects and wasted productive machining time. The new idea proposed in this thesis is to perform ILC on a virtual model, which is continuously updated via real-time production data using the identification methods developed in this work. This would minimize the amount of trial and error correction needed on the actual machine. In the course of this thesis research, after validating the effectiveness of ILC in simulations, to reliably and safely migrate the virtual modeling and trajectory correction results into industry (such as on a gear grinding machine tool), the author initiated and led the design and fabrication of an industry-scale testing platform, comprising a Siemens 840D SolutionLine CNC with a multi-axis feed drive setup. Majority of this implementation has been completed, and in near future work, the dynamic accuracy and productivity improvements facilitated with ‘virtually’ tuned ILC are expected to be demonstrated experimentally and tested in industry