The paper presents a case study on the application of supervised switched multiple model adaptive control (SMMAC) to drive the temperature in an air heating fan. The plant considered is of distributed parameter type and its linearized dynamics changes with the value of air flow. The compromises in the design of the different elements of SMMAC are discussed, with emphasis on the trade-off involved in selecting the observer poles. Experimental results show the impromevent in performance of SMMAC with respect to the use of a single linear controller.
K. Krumbiegel (University Duisburg-Essen, Duisburg, Germany)
A. Rosch (University Duisburg-Essen, Duisburg, Germany)
Linear quadratic optimal control problems governed by PDEs with pointwise control constraints are considered. We derive error estimates for feasible and infeasible controls of the problem. Based on this theory an error estimator is constructed for different discretization schemes. Moreo ver, we establish the estimator as a stopping criterion for several optimization methods. Furthermore, additional errors caused by solving the linear systems are discussed. The theory is illustrated by numerical examples.
keywords: linear quadratic optimal control problems, control constraints, error estimates, projected gradient method, primal-dual active set strategy, penalty methods, stopping criteria
T. Kaczorek (Bialystok Technical University, Bialystok, Poland)
The realization problem for positive fractional continuous-time linear systems is addressed. Sufficient conditions for the existence of positive realizations for continuous-time linear systems are established. Procedures for computation of positive fractional realizations for SISO and MIMO continuous-time linear systems are proposed and illustrated by numerical examples.
keywords: fractional, positive, realization, continuous-time linear system
W.P. Hunek (Opole University of Technology, Opole, Poland)
The paper presents a new contribution of the so-called control zeros to robustification of the minimum variance control strategy for nonsquare LTI MIMO systems. A plethora of new, MVC-related inverses of nonsquare polynomial matrices are analytically presented, which give rise to generation of various control zeros. Possible detrimental effects of unstable control zeros can be eliminated making use of a new, pole-free MVC design methodology, but on the other hand, one can take advantage of stable control zeros in a new, minimum-energy design of robust MVC. Thus, control zeros are shown to essentially complement the transmission zero-based Davison's theory of minimum phase nonsquare LTI MIMO systems.
keywords: robust minimum variance control, nonsquare systems, inverses of polynomial matrices, transmission zeros, control zeros, minimum energy
R. Matusu (Tomas Bata University in Zlin, Czech Republic)
R. Prokop (Tomas Bata University in Zlin, Czech Republic)
Systems with parametric uncertainty represent an important class of uncertain objects that are characterized by mathematical model containing parameters which are not precisely known, but the values thereof lie within given intervals. This type of uncertainty can arise during the control of real processes, e.g. as a consequence of imprecise measuring or of the influence of certain external conditions. If individual uncertain coefficients (in polynomial, in transfer function etc.) are mutually independent, the uncertainty has a simple interval structure. This article presents several possibilities of interval uncertainty for systems description as well as the tools for robust stability analysis, emphasizing advantages and limitations connected with the use of this simple structures, even for more complex problems.
A.M. Panda (Department of Electrical Engineering, NIT Rourkela-769008, Orissa, India)
S.R. Mohanty (Department of Electrical Engineering, NIT Rourkela-769008, Orissa, India)
P.K. Ray (Department of Electrical Engineering, NIT Rourkela-769008, Orissa, India)
B. Subudhi (Department of Electrical Engineering, NIT Rourkela-769008, Orissa, India)
An extended least square (ELS) technique has been proposed in this paper for power system frequency estimation. The validation of the above technique has been made by comparing its performance with the existing techniques such as Kalman filter (KF) and least mean square (LMS) technique etc. It has been observed through a series of simulation studies on frequency estimation that the ELS technique exhibits better performance in comparison to both the LMS and KF methods of power system frequency estimation. In Kalman filter, the determination of covariance matrix is very crucial leading to delay in convergence. LMS algorithm becomes complicated with the incorporation of correlation matrix, which may affect the convergence. On the contrary extended least square algorithm seems to be very simple and attractive without the implementation of covariance and correlation matrix. The feasibility of the ELS algorithm for frequency estimation has been tested with a signal buried with noise. The above estimation technique can be applied in real-time implementation, which will be immensely helpful for the power system protection. A comparative study on performance of the KF, LMS and ELS techniques for power system estimation has been made and included in the paper.
keywords: extended least square (ELS) technique, Kalman filter, least mean square (LMS) technique, power system parameters
M. Bouchoucha (LCC, Ecole Militaire Polytechnique, Algerie)
M. Tadjine (LCP, Ecole Nationale Polytechnique, Algerie)
A. Tayebi (ACL, Lakehead University, Thunder Bay, Canada)
P. Mullhaupt (ACL, Ecole Polytechnique Federale de Lausanne, Switzerland)
S. Bouabdallah (ASL, Swiss Federal Institute of Technology, Switzerland)
Based on the Euler angles parametrization, a new method for the attitude control of a vertical take-off and landing (VTOL) quadrotor aircraft is proposed. It relies on the combination of the backstepping technique and a nonlinear robust PI controller. The integral action gain is nonlinear and based on a switching function that allows a robust behavior for the overall control law. One of the strengths of the proposed approach is its robustness with respect to plant parameters uncertainties. The proposed approach has been tested in simulation and in real time and shows good performance.
P. Przyborowski (Warsaw University of Technology, Warsaw, Poland)
The positive linear fractional discrete-time Lyapunov systems are introduced. The necessary and sufficient conditions for the positivity, reachability, controllability to zero and observability of the systems are established. The sufficient conditions for stability are given. The notion of the dual positive fractional Lyapunov system is introduced and the relationship between the reachability and observability is given. The considerations are illustrated on the numerical example.