WSEAS Transactions on Systems and Control

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Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 8, 2013

Issue 1, Volume 8, January 2013

Title of the Paper: Delay-Dependent State Estimation for Time Delay Systems

Authors: Mohammad Ali Pakzad, Bijan Moaveni

Abstract: In this article, an observer with delay-dependent stability conditions has been presented for time delay systems with unknown inputs, where the time delay terms exist in the state and output of the system. The designing of this observer, whose performance index is the H2 norm, has been formulated as a nonlinear optimization problem. By using the finite characterization of a Lyapunov functional equation, sufficient conditions have been proposed to guarantee the existence of a desirable H2 filter. This finite characterization can be calculated by means of a matrix exponential function. Several numerical examples have also been simulated to show the effectiveness and simplicity of the proposed observer.

Keywords: Time delay system, Lyapunov functional, state delay system, H2 filter, observer, Kalman filter

Title of the Paper: A Flow-Based Approximation of Observer Error Linearization for Non-Linear Systems

Authors: Klaus Robenack

Abstract: This paper deals with observer design for non-linear single output systems. When a classical observer error linearization by output injection is not possible due to restrictive existence conditions, a simple approximation scheme is proposed. The method can be applied to a wider class of non-linear systems. Our approach is constructive and can be implemented using computer algebra packages. The design procedure is carried out for two example systems.

Keywords: Differential geometry, non-linear differential equations, observers

Title of the Paper: Co-Ordinated Average Consensus of Multi-agent Systems via Sampled Control

Authors: Yongli Cheng, Dongmei Xie

Abstract: This paper studies the co-ordinated average consensus of multi-agent system under Cartesian co-ordinate coupling in a discrete-time setting with switching sampling interval. Two cases are considered: 1) network without sampling delay; 2) network with sampling delay. For both cases, by algebraic graph theory and matrix theory, we analyze the convergence of the system and not only prove the existence of the sampling period, the Euler angle of the rotation matrix and sampling delay, but also give the approach of how to choose them. Our study shows that the eigenvalues of the corresponding Laplacian matrix, the size of the Euler angle, sampling period and delay have an important effect on consensus. Finally, some numerical simulations are presented to illustrate our theoretical results.

Keywords: Multi-agent systems, Cartesian co-ordinated coupling, average consensus, sampled control, switching sampling interval

Issue 2, Volume 8, April 2013

Title of the Paper: Invariant Sets in Sliding Mode Control Theory with Application to Servo Actuator System with Friction

Authors: Shibly Ahmed Al-Samarraie

Abstract: The mismatched perturbations and system chattering are the two main challenging problems in sliding mode control. This paper tries to solve these problems by deriving the invariant sets created by the sliding mode controller where the present work is devoted to a second order nonlinear affine system. If the state started in these sets it will not leave it for all future time. The first invariant set is found function to the initial condition only. Accordingly, the state bound is estimated and used when determining the gain of the sliding mode controller. This step overcomes an arithmetic difficulty that consists of calculating suitable controller gain value that ensures the attractiveness of the switching manifold with lower chattering behavior. Moreover to eliminate system chattering and to attenuate the effects of the mismatched perturbations, the signum function is replaced by an approximate form which yields a differentiable sliding mode controller. Therefore, the state will converge to a second positively invariant set rather than the origin. The size of this set, as derived here, is function to the parameters that can be chosen by the designer. This result enables us to control the size of the steady state error which means also that the effect of mismatched perturbation is attenuated. The sliding mode controller is then applied to the servo actuator system with friction based on the derived invariant sets. The friction model is represented by the major friction components; Coulomb friction, the Stiction friction, and the viscous friction. The simulation results demonstrate the rightness of the derived sets and the ability of the differentiable sliding mode controller to attenuate the friction effect and regulate the state to the positively invariant set with a prescribed steady state error.

Keywords: Positively Invariant Set, Sliding Mode Control, Servo Actuator, Friction Model

Title of the Paper: An Adaptive Block Backstepping Controller for Attitude Stabilization of a Quadrotor Helicopter

Authors: Hongtao Zhen, Xiaohui Qi, Hairui Dong

Abstract: A new block backstepping controller is proposed to solve the attitude stabilization problem for a quadrotor helicopter. The attitude kinematical model is obtained and translated into a MIMO nonlinear system with generalized uncertainties. Under the consideration of the coupling between the attitude angles, a nominal block backstepping controller is designed. The obtained controller is then augmented by a robust adaptive function to approximate the modeling errors and external disturbance. A nonlinear tracking-differentiator is applied to reduce computer explosion which is a ubiquitous problem in backstepping controllers. The closed-loop system is proved to be stable and exponential convergent through constructing appropriate Lyapunov function. Simulation results in the presence of external momentary disturbances and parametric uncertainties are presented to corroborate the effectiveness and the robustness of the proposed strategy.

Keywords: Quadrotor, Block Backstepping, Robust function, Adaptive control, tracking-differentiator

Title of the Paper: A Convex Optimization Approach to Control Design for Switching Power Converters with Time Delays

Authors: Mohammad Karimi

Abstract: In this paper a convex optimization approach to design a robust state feedback control is proposed for DC-DC converter systems with mixed delays. Based on the Lyapunov theory, some required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired control is derived based on a convex optimization method.

Keywords: Robust control, DC-DC converter, Lyapunov function, delay, LMI

 Issue 3, Volume 8, July 2013

Title of the Paper: Pole-Placement and LQ Hybrid Adaptive Control Applied Isothermal Continuous Stirred Tank Reactor

Authors: Jiri Vojtesek, Petr Dostal

Abstract: The paper deals with simulation experiments on the nonlinear system represented by the isothermal continuous stirred tank reactor. At first, the mathematical model derived from the material balances inside the reactor will be introduced and then the steady-state and the dynamic analyses were performed on this model. As a result of these studies, the optimal working point and the choice of the external linear model for the identification will be obtained. The spectral factorization with pole-placement method and linear-quadratic approach were employed in the controller design and computation. Both types of adaptive controllers have parameters for tuning of the output response. Moreover, controllers have satisfied basic control requirements such as the stability, the reference signal tracking and the disturbance attenuation.

Keywords: Steady-state, dynamic analysis, polynomial approach, Pole-placement method, LQ, recursive identification, adaptive control

Title of the Paper: Modeling and Analysis of Multi-Phase Inverter Fed Induction Motor Drive with Different Phase Numbers

Authors: G. Renukadevi, K. Rajambal

Abstract: This paper presents a modeling and analysis of multi-phase inverter fed multi-phase induction motor drive with different number of phases. Multiphase induction motor drives possess several advantages over conventional three-phase drives such as lower torque pulsation, fault tolerance, stability, high efficiency and lower current ripple and reduced current per phase without increasing voltage per phase etc., In this paper, a detailed d-q modeling of multi-phase induction motor drive with offset injection method based multi-phase VSI is developed. The simulation results are presented for 3, 5, 7, 9 and 11 phase induction motor under varying load conditions. The performance of the drive is analyzed in terms of stator current, power, torque ripple and fault tolerant feature respectively. Feasibility of the developed approach has been identified with the optimum number of phases for electric vehicle applications.

Keywords: Dynamic response, EV (Electric Vehicle), fault-tolerant feature, multi-phase drive, Switching technique, transient response

Title of the Paper: Single-Phase M-Channel Interleaved and N-Switch Paralleled Power Factor Corrector using EL Model Passivity Control

Authors: Wang Nan, Lu Fei, Yang Xi-Jun, Liu Ming-Lin, Lei Huai-Gang

Abstract: For high-power home inverter air conditioners and other electrical equipment which are supplied by single-phase AC power source, single-phase power factor correction (APFC) is needed. For example, multi-level interleaved APFC or single-level APFC with multiple power devices in parallel. This paper proposes a new single-phase M level and N power devices in parallel PFC which is driven by shift phase control method. Then the paper analysis its circuit structure and working principle, including voltage transformation ratio, ripple current, driving method and control methods. This MN APFC can transmit high power and reduce the switching frequency of the power devices. This circuit structure simplifies the selection of power devices. Meanwhile, it can also maintain the operating frequency of the boost inductor unchanged or maintain the switching frequency of the power device constant. This control method improves the operating frequency of the boost inductor several times and simplifies the inductor design. This paper establishes the EL (Euler-Lagrange) mathematical model of MN PFC which is working in continuous conduction mode (CCM) based on its power circuit. The passivity of MN PFC is proved and passivity-based controller using stated variables feedback, damping injection method is designed in this paper. The proposed control scheme which don't need proportion integral controller has strong robustness on disturbance of input voltage, load and parameters of system components. Especially in applications of wide range load, the dynamic response of input current is very fast and the output voltage almost has no changes so that the power factor correction and constant DC output functions of PFC are realized. Meanwhile, MN PFC employing passivity-based controller has a good effect on current sharing. Then, as 2x2 PFC for example, this method is simulated and analyzed by MATLAB/SIMULINK. Simulation results show that the passivity-based controller has a superior performance and the method is feasible.

Keywords: Power factor correction, two-channel interleaved, two-device paralleled, phase-shifted driving, passivity-based control, current sharing

Title of the Paper: Control Algorithms with Suppression of Measurable Disturbances: Comparison of Two Methods

Authors: Marek KubalĨík, Vladimír Bobál

Abstract: Many processes are affected by external disturbances caused by the variation of variables that can be measured. This paper compares two control strategies which are suitable for rejection of measurable disturbances. The first method which can successfully handle known measurable disturbances is model predictive control (MPC). Known disturbances can be taken explicitly into account in predictive control. Two different approaches to computation of multi–step–ahead predictions incorporating known measurable disturbances into prediction equations are proposed. The second control algorithm is designed using polynomial theory developed for linear controlled systems. Both methods are based on a same model of a controlled process. Simulation results are also included and quality of control achieved by both methods is compared and discussed.

Keywords: Predictive control, Polynomial methods, Disturbance rejection, Diophantine equations, Prediction, CARIMA model

Title of the Paper: 4D Trajectory Generation and Tracking for Waypoint-Based Aerial Navigation

Authors: K. Bousson, Paulo F. F. Machado

Abstract: One of the operational requirements for unmanned aerial vehicles is the autonomous navigation and control along a given sequence of waypoints, or along a predefined trajectory. Existing autonomous navigation procedures are mostly done in 3D because of the stringent certification requirements for 4D flight and due to the complexity in coping with time of arrival at waypoints, whilst actual flight plan fulfillment requires 4D navigation. The present paper deals with the 4D navigation trajectory generation and tracking of unmanned aerial vehicles along given sequences of waypoints with arrival time constraints at each of these waypoints. The approach that is used is twofold, first an optimal continuous trajectory is generated passing through the sequence of waypoints using the pseudospectral based trajectory optimization method, and then a predictive control law is used to drive the aircraft along the generated trajectory with minimum deviation. The proposed method for trajectory generation does not require slack variables to deal with the waypoints nor does it resort to the flight dynamics equations; thus the complexity of the underlying computation procedure is qualitatively lower than currently used methods. The method is successfully validated on two realistic cases giving better results than other conventional methods used in waypoint-based trajectory generation.

Keywords: Trajectory optimization, waypoint navigation, 4D trajectory, pseudospectral approximation, predictive control

Issue 4, Volume 8, October 2013

Title of the Paper: Sensor Scheduling for Target Tracking Using Approximate Dynamic Programming

Authors: Zining Zhang, Ganlin Shan

Abstract: To trade off tracking accuracy and interception risk in a multi-sensor multi-target tracking context, we study the sensor-scheduling problem where we aim to assign sensors to observe targets over time. Our problem is formulated as a partially observable Markov decision process, and this formulation is applied to develop a non-myopic sensor-scheduling scheme. We resort to extended Kalman filtering for information-state estimation and use unscented transformation for trajectory sampling in order to reduce the number of samples required for Q-value approximation. We make decision using a simulation-based approximate dynamic programming method called policy rollout, which is implemented by means of receding horizon control. The effectiveness of our approach is substantiated through an example in which multiple sensors are deployed to track a single target.

Keywords: Non-myopic sensor scheduling, Partially observable Markov decision process, Interception risk, Policy rollout, Unscented transformation

Title of the Paper: Control Design of a Nonlinear Multivariable Process

Authors: Petr Dostal, Vladimir Bobal, Jiri Vojtesek

Abstract: The paper presents an effective procedure for control design of multi input – multi output nonlinear processes. The procedure is based on an approximation of a nonlinear model of the process by a continuoustime external linear model in the form of the left polynomial matrix fraction. The parameters of the continuoustime external linear model are recursively estimated either by a direct method or through an external delta model. The control system structure with two feedback controllers is used. The controllers are derived using the explicit pole assignment method. The control is simulated on the nonlinear model of two conic liquid tanks in series.

Keywords: Nonlinear system, multivariable system, polynomial matrix, external linear model, delta model, polynomial approach, pole assignment

Title of the Paper: Deterministic and Stochastic Advertising Diffusion Model with Delay

Authors: Nicoleta Sirghi, Mihaela Neamtu

Abstract: This paper analysis an advertising diffusion model. A firm launches a new product and devotes a fixed proportion of sales to advertising, while customers go through a three stage adoption process with some delay, on the effect of advertisement. The mathematical model is described by a nonlinear differential system with delay. We set the condition for the existence of the delay parameter value for which the model displays a Hopf bifurcation. The direction and the stability of the Hopf bifurcation is done. The stochastic case is taken into consideration. The last part of the paper includes numerical simulations and conclusions.

Keywords: Advertising diffusion model, bifurcation theory, Hopf bifurcation, stability

Title of the Paper: Reduced-Order Observer-based Containment Control of General Linear Multi-agent Systems With Multiple Interaction Leaders

Authors: Fang Yan, Dongmei Xie

Abstract: This paper investigates the reduced-order observer-based containment control problems of general linear multi-agent systems (MASs) with multiple interaction leaders. Assuming that (A, B, C) is stabilizable and detectable and the directed graph is weakly connected, we establish the necessary and sufficient containment control criteria for continuous-time MASs and discrete-time MASs, respectively. Our main results show that the eigenvalues of the Laplacian matrix, the communication topology graph, the selection of protocol parameters and gain matrices play an important role in the achievement of containment control. Finally, numerical simulations are given to illustrate our main results.

Keywords: Containment control; Consensus; Reduced-order observer; General linear system