I. Automatic Control and Systems Modeling
On the Cancelation of Decoupling Zeros at s = ∞
A.I.G. Vardulakis and M. Rapti
Aristotle Univ. of
Abstract: We examine the mechanism of cancelations of decoupling zeros at infinity of a left polyniomial matrix description (left PMD) of a linear multivariale system. It is shown that a theory completly analogus to the classical Rosenbrock-Wolovich theory regarding the cancelation of nite decoupling zeros can be formulated. The whole theory is illustrated by a simple example.
Second Order Sliding Mode Control of Nonlinear Multivariable Systems
Inst. of Intelligent
Systems for Automation,
Abstract: The paper proposes an approach to second order sliding mode control for multi-input multi-output (MIMO) nonlinear uncertain systems. With respect to standard sliding mode control, the second order sliding mode techniques for singleinput single-output (SISO) systems show the same properties of robustness and precision, feature a higher order accuracy and can be exploited to eliminate the chattering effect. The extension of these results to the MIMO nonlinear systems is a challenging matter. In the present paper, the validity is extended to a quite large class of nonlinear processes affected by uncertainties of general nature; the control design is simple; the conditions of existence on the controllers are weak. The proposed procedure represents a general approach to the second order sliding mode control of MIMO systems.
Nonlinear Predictive Adaptive Controllers for General Nonlinear Systems
M. Mrabet1, F. Fnaiech1 and K. Al-Haddad2
1Ecole Supérieure des Sciences et Techniques de Tunis, Tunisia, 2Chaire de Recherche du Canada, Canada
Abstract: In this paper, we propose a new model reference adaptive predictive controller scheme for general non linear systems using analytic linearization. When the parameters used in the design of the predictive controller are unknown and time-varying, adaptive tools became very necessary in designing the controller. The adaptation of the parameters is calculated by the minimization of the predictive error in the receding horizon using a Taylor series expansion. To demonstrate the efficiency of the proposed scheme a comparison of the predictive algorithm with fixed gain elaborated by  and the adaptive proposed scheme are presented as illustrative example.
Minimal Covering with Stability
Technol. Education Inst.
Abstract: In this paper we solve two problems. For systems with one input first we find all the A modulo B invariant subspaces of given dimension that cover a given space and second we find among them those that are stable.
Realization Problem for Positive Multivariable Continuous-Time Systems with Delays
Abstract: The realization problem for positive, multivariable continuous-time linear systems with delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for computation of positive minimal realizations is presented and illustrated by an example.
Revision on the Strict Positive Realness
M. Hakimi-M1 and H. Khaloozadeh2
Abstract: In this paper, the necessary and sufficient conditions for strict positive realness of the real rational transfer functions are studied directly from basic definitions in the frequency domain. This paper deals with a new frequency domain approach to check if a real rational transfer function is a strictly positive real or not. This approach is based on the Taylor expansion and the Maximum Modulus Principle which are the fundamental tools in the complex analysis. Four related predominant statements in the strict positive realness area which is appeared in the control literature are discussed; the weaknesses and the drawbacks of these predominant statements are analyzed through some counter examples. Then a new necessary condition for strict positive realness are extracted via high frequency behavior of the Nyquist diagram. Finally the most simplified and completed conditions for strict positive realness are presented based on the complex analysis.
A Complete 3-D Canonical Piecewise-Linear Representation
C. Wen and S. Wang
Abstract: A complete 3-D Canonical Piecewise-Linear (CPWL) representation is developed constructively in this paper. The key to the representation is the establishment of the explicit functional formulation of basis function. It is proved that basis function is the most elementary generating function from which a fully general 3-D PWL function can be formulated. This CPWL representation laid a solid theoretical foundation for the development of a general nonlinear approximation, which can be seen as an extended version of the well-established Hinging Hyperplane Algorithm.
The TOR Design for the Optimal control of Linear Systems
1Technol. Education Inst. of
Abstract: In this paper the theoretical base and practical application of the TOR design for the control of linear systems is presented. This method is based on the synergy of the LQG balancing and Persson-Astrom (PA) methods for the design of optimal controllers. LQG balancing is a base for the order reduction of linear systems, whose processes and measurements are affected by white noise. The Persson-Astrom (PA) method is a base for the tuning of PID controllers. The method of calculation of the LQG controller is presented, in which the Riccati equations and Kalman estimator are used. The superiority of the TOR idea: the simultaneous use and interconnection of PA-PID tuning and LQG method is pointed out, by its comparison to the single use of the PID approach and LQG approach, which are provided in the MATLAB demo for the control of angular velocity of a DC motor exposed to external disturbances (torque Td). The control strength of various methods is presented at the comparative diagram developed by programming in the MATLAB environment.
Heterarchical Distributed State Estimation and Failure Detection in Dynamic Systems
R.B. Quirino1, and C.P. Bottura2
Abstract: In this paper we discuss a class of failure detection techniques that is based on the heterarchical distributed state estimation structure. A heterarchical structure is defined as a data processing system in which there is no explicit hierarchy. Within this discussion, we present a distributed sensor fault detection and isolation method that results from merging hierarchical state estimation theory with the overlapping decompositions, expansions, and stability of large scale systems theory. The benefits of such a discussion include to have design methodologies of detection, isolation and diagnosis of sensor faults, that admits a range of implementations, allowing a tradeoff study of system complexity vs. performance.
Stochastic/Adaptive Sliding Mode Observer for Noisy Excessive Uncertainties Nonlinear Systems
R. Raoufi1 and H. Khaloozadeh2
Abstract: A robust/adaptive stochastic observer is presented for stochastic nonlinear dynamics having excessive uncertainties. It was shown through a new theorem that the proposed nonlinear robust sliding mode observer has very accurate state estimate error characteristic. The observer uses the sliding mode technique for the robustness and a deterministic adaptive law to guarantees a globally asymptotically convergence observation error. Finally, an example is given to illustrate the application and very favorable convergence properties of the proposed observer.
Quasi-Min-Max MPC with Linear
Z.Q. Zou1, L.H. Xu1 and M. Yuan2
Abstract: Controlled invariance terminal region and associated feedback law are important in model predictive control of constrained systems, since large terminal region implies large region of stable initial conditions. In this paper, the polytopic invariance terminal region is designed instead of former ellipsoid terminal region, which enables greater flexibility in the shape of terminal region and could enlarge the invariance terminal region; at the same time the linear parameter-dependent state feedback law inside terminal region is designed instead of only the state feedback law, which enables higher degree of the feedback law and enlarges the invariance terminal region. In addition, one horizon free control is designed by utilizing real-time measured parametervarying state space matrices, which enlarges the region of stable initial conditions and reduces the performance. Simulation expounds these characteristics.
Nonlinear Control Strategies Incorporating Input-State-Output Models
City Liberal Studies,
Abstract: Dynamic recurrent neural networks have become popular for use in nonlinear control due to recent developments concerning their use in control strategies such as the Internal Model Control (IMC) and Global Linearisation Control (GLC). In both strategies a neural network is used to model the nonlinear plant, and from this model a control rule is formulated so that the cascaded system of plantmodelcontroller becomes linear in behaviour. Investigators have referred to IMC as an inputoutput approach and GLC as an inputstateoutput approach. It has been speculated that there exist and equivalence in these two strategies. In this paper we examine both control strategies and demonstrate the conditions under which the two are equivalent. The conditions are tested in simulations by implementing the two strategies to control a simple nonlinear plant, using first an exact model of the plant, then a model that contains some errors and finally with a dynamic recurrent neural network that has been trained as a model of the plant.
Robust Optimal Tracking Control of Hybrid Systems: Based on Dynamical Programming
L. Lin, C. Yangzhou and C. Pingyuan
Abstract: This paper studies the optimal tracking problem for LTI switched system.A linear quadratic error criterion is used as the cost function.Firstly,Based on the dynamical programming, the optimal tracking algorithm is designed.Secondly, the stability analysis of this feedback optimal tracking problem is discussed.Then,faced with nonlinear uncertainty of statistics in dynamic switched systems the robust stability condition of linear-quadratic optimal tracking problems is obtained .At last, a numerical example shows the main algorithm we designed.
A Combined QFT/EEAS Design Technique for Uncertain Multivariable Plants
O. Namaki-Shoushtari1, A. Khaki-Sedigh2 and B.N. Araabi1
Abstract: This paper presents a robust-adaptive control design for uncertain multivariable plants based on Quantitative Feedback Theory (QFT) and Externally Excited Adaptive Systems (EEAS). Design requirements are derived and formulated in terms of different cost functions. Also, a stochastic optimization technique is employed to optimally design the overall robust adaptive controller. This controller can handle large plant parameter uncertainties with lower control gains. Simulation results are provided to show the effectiveness and features of the proposed QFT/EEAS MIMO design methodology compared with the direct MIMO QFT design approach.
A State-Space Approach for Analysing the Bullwhip Effect in Supply Chains
C. Papanagnou and G. Halikias
Abstract: The bullwhip effect is a well known instability phenomenon in supply chains, related to volatility amplification of demand profiles in the upper nodes of the chain. We propose a novel state-space approach for analysing a simple series supply chain model with an arbitrary number of nodes. In addition, we develop techniques for calculating explicitly the associated covariance matrix in parametric form, under white-noise demand profile assumptions. This allows us to analyze the effect of a parameter in the studied inventory policies on the bullwhip effect for chains with an arbitrary number of nodes.
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