Search results for: Non Linear Control

Authors: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: S. Anbu, N. Jaya

Abstract:

Nonlinearity is the inherent characteristics of all the industrial processes. The Classical control approach used for a generation often fails to show better results particularly for non-linear systems and in the systems, whose parameters changes over a period of time for a variety of reasons. Alternatively, adaptive control strategies provide very good performance. The Model Reference Adaptive Control based on Lyapunov stability analysis and classical PI control strategies are designed and evaluated for Continuous Stirred Tank Reactor, which shows appreciable dynamic nonlinear characteristics.

Keywords: Adaptive Control, CSTR, Lyapunov stability, MRAS, PID.

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Authors: Omid S. Fard, Akbar H. Borzabadi

Abstract:

In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, Linear programming.

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

Abstract:

The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: Smart material, on-line differential artificial neural network, active control, finite element method.

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Authors: M. Zareiee, A. Dideban

Abstract:

This paper addresses the problem of forbidden states in non safe Petri Nets. In the system, for preventing it from entering the forbidden states, some linear constraints can be assigned to them. Then these constraints can be enforced on the system using control places. But when the number of constraints in the system is large, a large number of control places must be added to the model of system. This concept complicates the model of system. There are some methods for reducing the number of constraints in safe Petri Nets. But there is no a systematic method for non safe Petri Nets. In this paper we propose a method for reducing the number of constraints in non safe Petri Nets which is based on solving an integer linear programming problem.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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Authors: Boukhzer Abdenbi, El Bikri Khalid, Benamar Rhali

Abstract:

In the present study, the problem of geometrically non-linear free vibrations of functionally graded rectangular plates (FGRP) is studied. The theoretical model, previously developed and based on Hamilton’s principle, is adapted here to determine the fundamental non-linear mode shape of these plates. Frequency parameters, displacements and stress are given for various power-law distributions of the volume fractions of the constituents and various aspect ratios. Good agreement with previous published results is obtained in the case of linear and non-linear analyses.

Keywords: Non-linear vibration, functionally graded materials, rectangular plates.

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

Abstract:

This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.

Keywords: Microgrids, secondary control, multiagent, sampling, LMI.

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Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

Abstract:

In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: Autonomous vehicles, convoy, nonlinear control, nonlinear observer, sliding mode.

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Authors: Ishapathik Das

Abstract:

The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.

Keywords: Model misspecification, multivariate kriging, multivariate logistic link, ordinal response models, quantile dispersion graphs.

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Authors: Shiang-Hwua Yu, Han-Sheng Tseng

Abstract:

This paper presents a novel sinusoidal modulation scheme that features least correlated noise and high linearity. The modulation circuit, which is composed of a quantizer, a resonator, and a comparator, is capable of eliminating correlated modulation noise while doing modulation. The proposed modulation scheme combined with the linear quadratic optimal control is applied to a single-phase voltage source inverter and validated with the experiment results. The experiments show that the inverter supplies stable 60Hz 110V AC power with a total harmonic distortion of less than 1%, under the DC input variation from 190 V to 300 V and the output power variation from 0 to 600 W.

Keywords: Pulse width modulation, feedback dithering, linear quadratic control, inverter.

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Authors: R. Khaniki, M.B. Menhaj, H. Eliasi

Abstract:

This paper describes the application of a model predictive controller to the problem of batch reactor temperature control. Although a great deal of work has been done to improve reactor throughput using batch sequence control, the control of the actual reactor temperature remains a difficult problem for many operators of these processes. Temperature control is important as many chemical reactions are sensitive to temperature for formation of desired products. This controller consist of two part (1) a nonlinear control method GLC (Global Linearizing Control) to create a linear model of system and (2) a Model predictive controller used to obtain optimal input control sequence. The temperature of reactor is tuned to track a predetermined temperature trajectory that applied to the batch reactor. To do so two input signals, electrical powers and the flow of coolant in the coil are used. Simulation results show that the proposed controller has a remarkable performance for tracking reference trajectory while at the same time it is robust against noise imposed to system output.

Keywords: Generalized Predictive Control (GPC), TemperatureControl, Global Linearizing Control (GLC), Batch Reactor.

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Authors: R. Khaniki, M.B. Menhaj, H. Eliasi

Abstract:

This paper describes the application of a model predictive controller to the problem of batch reactor temperature control. Although a great deal of work has been done to improve reactor throughput using batch sequence control, the control of the actual reactor temperature remains a difficult problem for many operators of these processes. Temperature control is important as many chemical reactions are sensitive to temperature for formation of desired products. This controller consist of two part (1) a nonlinear control method GLC (Global Linearizing Control) to create a linear model of system and (2) a Model predictive controller used to obtain optimal input control sequence. The temperature of reactor is tuned to track a predetermined temperature trajectory that applied to the batch reactor. To do so two input signals, electrical powers and the flow of coolant in the coil are used. Simulation results show that the proposed controller has a remarkable performance for tracking reference trajectory while at the same time it is robust against noise imposed to system output.

Keywords: Generalized Predictive Control (GPC), TemperatureControl, Global Linearizing Control (GLC), Batch Reactor.

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Authors: Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shehzad, Israr Ahmad

Abstract:

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.

Keywords: Nonlinear Active Control, Chen and Tigan Chaotic systems, Lyapunov Stability theory, Synchronization.

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Authors: M. Polanský

Abstract:

This paper introduces a new method called ARPDC (Advanced Robust Parallel Distributed Compensation) for automatic control of nonlinear systems. This method improves a quality of robust control by interpolating of robust and optimal controller. The weight of each controller is determined by an original criteria function for model validity and disturbance appreciation. ARPDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy systems and Parallel Distributed Compensation (PDC) control scheme. The relaxed stability conditions of ARPDC control of nominal system have been derived. The advantages of presented method are demonstrated on the inverse pendulum benchmark problem. From comparison between three different controllers (robust, optimal and ARPDC) follows, that ARPDC control is almost optimal with the robustness close to the robust controller. The results indicate that ARPDC algorithm can be a good alternative not only for a robust control, but in some cases also to an adaptive control of nonlinear systems.

Keywords: Robust control, optimal control, Takagi–Sugeno (TS) fuzzy models, linear matrix inequality (LMI), observer, Advanced Robust Parallel Distributed Compensation (ARPDC).

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Authors: Jan Erik Stellet

Abstract:

This article presents a detailed analysis and comparative performance evaluation of model reference adaptive control systems. In contrast to classical control theory, adaptive control methods allow to deal with time-variant processes. Inspired by the works [1] and [2], two methods based on the MIT rule and Lyapunov rule are applied to a linear first order system. The system is simulated and it is investigated how changes to the adaptation gain affect the system performance. Furthermore, variations in the reference model parameters, that is changing the desired closed-loop behaviour are examinded.

Keywords: Adaptive control systems, Adaptation gain, MIT rule, Lyapunov rule, Model reference adaptive control.

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Authors: M. Kusá, M. Matúšová, A. Javorová, K. Velí

Abstract:

This paper deals about four items assembly process of linear drive. This assembly will be realized in flexible assembly cell on Institute of Manufacturing Systems and Applied Mechanics. There is defined manufacturing cell, individual actuators created our flexible cell. Next chapter is about control type, detailed describe a sequence control type, which will be used in mentioned flexible assembly cell. All cell control is divided in individual steps instructions. There instructions illustrate table number III.

Keywords: assembly, flexible cell, sequence control

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Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

Abstract:

In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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Authors: M. Ouassaid, A. Nejmi, M. Cherkaoui, M. Maaroufi

Abstract:

The very nonlinear nature of the generator and system behaviour following a severe disturbance precludes the use of classical linear control technique. In this paper, a new approach of nonlinear control is proposed for transient and steady state stability analysis of a synchronous generator. The control law of the generator excitation is derived from the basis of Lyapunov stability criterion. The overall stability of the system is shown using Lyapunov technique. The application of the proposed controller to simulated generator excitation control under a large sudden fault and wide range of operating conditions demonstrates that the new control strategy is superior to conventional automatic voltage regulator (AVR), and show very promising results.

Keywords: Excitation control, Lyapunov technique, non linearcontrol, synchronous generator, transient stability, voltage regulation.

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Authors: J. Ritonja

Abstract:

Available commercial applications of power system stabilizers assure optimal damping of synchronous generator’s oscillations only in a small part of operating range. Parameters of the power system stabilizer are usually tuned for the selected operating point. Extensive variations of the synchronous generator’s operation result in changed dynamic characteristics. This is the reason that the power system stabilizer tuned for the nominal operating point does not satisfy preferred damping in the overall operation area. The small-signal stability and the transient stability of the synchronous generators have represented an attractive problem for testing different concepts of the modern control theory. Of all the methods, the adaptive control has proved to be the most suitable for the design of the power system stabilizers. The adaptive control has been used in order to assure the optimal damping through the entire synchronous generator’s operating range. The use of the adaptive control is possible because the loading variations and consequently the variations of the synchronous generator’s dynamic characteristics are, in most cases, essentially slower than the adaptation mechanism. The paper shows the development and the application of the self-tuning power system stabilizer based on recursive least square identification method and linear quadratic regulator. Identification method is used to calculate the parameters of the Heffron-Phillips model of the synchronous generator. On the basis of the calculated parameters of the synchronous generator’s mathematical model, the synthesis of the linear quadratic regulator is carried-out. The identification and the synthesis are implemented on-line. In this way, the self-tuning power system stabilizer adapts to the different operating conditions. A purpose of this paper is to contribute to development of the more effective power system stabilizers, which would replace currently used linear stabilizers. The presented self-tuning power system stabilizer makes the tuning of the controller parameters easier and assures damping improvement in the complete operating range. The results of simulations and experiments show essential improvement of the synchronous generator’s damping and power system stability.

Keywords: Adaptive control, linear quadratic regulator, power system stabilizer, recursive least square identification.

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Authors: Bakari M. M. Mwinyiwiwa, Mighanda J. Manyahi, Nicodemu Gregory, Alex L. Kyaruzi

Abstract:

Microgrids are increasingly being considered to provide electricity for the expanding energy demand in the grid distribution network and grid isolated areas. However, the technical challenges associated with the operation and controls are immense. Management of dynamic power balances, power flow, and network voltage profiles imposes unique challenges in the context of microgrids. Stability of the microgrid during both grid-connected and islanded mode is considered as the major challenge during its operation. Traditional control methods have been employed are based on the assumption of linear loads. For instance the concept of PQ, voltage and frequency control through decoupled PQ are some of very useful when considering linear loads, but they fall short when considering nonlinear loads. The deficiency of traditional control methods of microgrid suggests that more research in the control of microgrids should be done. This research aims at introducing the dq technique concept into decoupled PQ for dynamic load demand control in inverter interfaced DG system operating as isolated LV microgrid. Decoupled PQ in exact mathematical formulation in dq frame is expected to accommodate all variations of the line parameters (resistance and inductance) and to relinquish forced relationship between the DG variables such as power, voltage and frequency in LV microgrids and allow for individual parameter control (frequency and line voltages). This concept is expected to address and achieve accurate control, improve microgrid stability and power quality at all load conditions.

Keywords: Decoupled PQ, microgrid, multisource, renewable energy, dq control.

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Authors: J. Ritonja, R. Brezovnik, M. Petrun, B. Polajžer

Abstract:

Many modern synchronous generators in power systems are extremely weakly damped. The reasons are cost optimization of the machine building and introduction of the additional control equipment into power systems. Oscillations of the synchronous generators and related stability problems of the power systems are harmful and can lead to failures in operation and to damages. The only useful solution to increase damping of the unwanted oscillations represents the implementation of the power system stabilizers. Power system stabilizers generate the additional control signal which changes synchronous generator field excitation voltage. Modern power system stabilizers are integrated into static excitation systems of the synchronous generators. Available commercial power system stabilizers are based on linear control theory. Due to the nonlinear dynamics of the synchronous generator, current stabilizers do not assure optimal damping of the synchronous generator’s oscillations in the entire operating range. For that reason the use of the robust power system stabilizers which are convenient for the entire operating range is reasonable. There are numerous robust techniques applicable for the power system stabilizers. In this paper the use of sliding mode control for synchronous generator stability improvement is studied. On the basis of the sliding mode theory, the robust power system stabilizer was developed. The main advantages of the sliding mode controller are simple realization of the control algorithm, robustness to parameter variations and elimination of disturbances. The advantage of the proposed sliding mode controller against conventional linear controller was tested for damping of the synchronous generator oscillations in the entire operating range. Obtained results show the improved damping in the entire operating range of the synchronous generator and the increase of the power system stability. The proposed study contributes to the progress in the development of the advanced stabilizer, which will replace conventional linear stabilizers and improve damping of the synchronous generators.

Keywords: Control theory, power system stabilizer, robust control, sliding mode control, stability, synchronous generator.

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Authors: Om Prakash Verma, Rajesh Singla, Rajesh Kumar

Abstract:

Conventional controller’s usually required a prior knowledge of mathematical modelling of the process. The inaccuracy of mathematical modelling degrades the performance of the process, especially for non-linear and complex control problem. The process used is Water-Bath system, which is most widely used and nonlinear to some extent. For Water-Bath system, it is necessary to attain desired temperature within a specified period of time to avoid the overshoot and absolute error, with better temperature tracking capability, else the process is disturbed.

To overcome above difficulties intelligent controllers, Fuzzy Logic (FL) and Adaptive Neuro-Fuzzy Inference System (ANFIS), are proposed in this paper. The Fuzzy controller is designed to work with knowledge in the form of linguistic control rules. But the translation of these linguistic rules into the framework of fuzzy set theory depends on the choice of certain parameters, for which no formal method is known. To design ANFIS, Fuzzy-Inference-System is combined with learning capability of Neural-Network.

It is analyzed that ANFIS is best suitable for adaptive temperature control of above system. As compared to PID and FLC, ANFIS produces a stable control signal. It has much better temperature tracking capability with almost zero overshoot and minimum absolute error.

Keywords: PID Controller, FLC, ANFIS, Non-Linear Control System, Water-Bath System, MATLAB-7.

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Authors: A. Ramdane, F.Naceri, S. Ramdane

Abstract:

in this work, we present a new strategy of direct adaptive control denoted: Extended minimal controller synthesis (EMCS). This algorithm is designed for an induction motor, which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The main motivation of the EMCS control is to enhance the robustness of the MRAC algorithms, i.e. the rejection of bounded effects of rapidly varying external disturbances.

Keywords: Adaptive Control, Simple model reference adaptive control (SMRAC), Extended Minimal Controller synthesis (EMCS), Induction Motor (IM)

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Authors: Sangbum Park, Youngjoon Han

Abstract:

This paper proposes a balance control scheme for a biped robot to trace an arbitrary path using image information. While moving, it estimates the zero moment point(ZMP) of the biped robot in the next step using a Kalman filter and renders an appropriate balanced pose of the robot. The ZMP can be calculated from the robot's pose, which is measured from the reference object image acquired by a CCD camera on the robot's head. For simplifying the kinematical model, the coordinates systems of individual joints of each leg are aligned and the robot motion is approximated as an inverted pendulum so that a simple linear dynamics, 3D-LIPM(3D-Linear Inverted Pendulum Mode) can be applied. The efficiency of the proposed algorithm has been proven by the experiments performed on unknown trajectory.

Keywords: Biped robot, Zero moment point, Balance control, Kalman filter.

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim

Abstract:

In this paper, application of Sliding Mode Control (SMC) technique for an Active Magnetic Bearing (AMB) system with varying rotor speed is considered. The gyroscopic effect and mass imbalance inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Transformation of the AMB dynamic model into regular system shows that these gyroscopic effect and imbalance lie in the mismatched part of the system. A H2-based sliding surface is designed which bound the mismatched parts. The solution of the surface parameter is obtained using Linear Matrix Inequality (LMI). The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.

Keywords: Active magnetic bearing, sliding mode control, linear matrix inequality, mismatched uncertainty and imbalance.

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Authors: H. Y. Jung, Ju H. Park, S. M. Lee

Abstract:

Sampled-data controller is presented for solid oxide fuel cell systems which is expressed by a sector bounded nonlinear model. The proposed control law is obtained by solving a convex problem satisfying several linear matrix inequalities. Simulation results are given to show the effectiveness of the proposed design method.

Keywords: Sampled-data control, Sector bound, Solid oxide fuel cell, Time-delay.

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

Abstract:

Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: Non-Linear Wilcoxon, robust estimation, Variogram estimation.

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Authors: Yash Pal, A.Swarup, Bhim Singh

Abstract:

This paper presents a novel control strategy of a threephase four-wire Unified Power Quality (UPQC) for an improvement in power quality. The UPQC is realized by integration of series and shunt active power filters (APFs) sharing a common dc bus capacitor. The shunt APF is realized using a thee-phase, four leg voltage source inverter (VSI) and the series APF is realized using a three-phase, three leg VSI. A control technique based on unit vector template technique (UTT) is used to get the reference signals for series APF, while instantaneous sequence component theory (ISCT) is used for the control of Shunt APF. The performance of the implemented control algorithm is evaluated in terms of power-factor correction, load balancing, neutral source current mitigation and mitigation of voltage and current harmonics, voltage sag and swell in a three-phase four-wire distribution system for different combination of linear and non-linear loads. In this proposed control scheme of UPQC, the current/voltage control is applied over the fundamental supply currents/voltages instead of fast changing APFs currents/voltages, there by reducing the computational delay and the required sensors. MATLAB/Simulink based simulations are obtained, which support the functionality of the UPQC. MATLAB/Simulink based simulations are obtained, which support the functionality of the UPQC.

Keywords: Power Quality, UPQC, Harmonics, Load Balancing, Power Factor Correction, voltage harmonic mitigation, currentharmonic mitigation, voltage sag, swell

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Authors: Dursun Aydın, Bilgin Senel

Abstract:

In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

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