Lyapunov based proportional-derivative observer

Bu tezde, doğrusal matris eşitsizlikleri kullanılarak literatürde mevcut Luenberger gözlemleyicisi ile tezde oluşturulan türevsel gözlemleyici tasarımları verilmiştir. Literatürde tanımlayıcı(descriptor) sistemler için mevcut Oransal-Türevsel gözlemleyicinin doğrusal matris eşitsizlikleri ile tasarımının mümkün olmadığı, bunun yerine çiftdoğrusal matris eşitsizliklerinin kullanılması gerektiği gösterilmiştir. Matris eşitsizlikleri ile verilen Luenberger, türevsel ve Oransal-Türevsel gözlemleyici modellerinden kestirim performansını iyileştirmek amacıyla gözlemleyicinin oluşturduğu çıkış işareti modellerden çıkarılmıştır. Oluşan yeni oransal, türevsel ve Oransal-Türevsel gözlemleyici modelleri için tasarım yöntemleri sunulmuştur. Bu gözlemleyicilerden yeni Oransal-Türevsel gözlemleyici n. dereceden Oransal-Türevsel gözlemleyici olarak kullandığı çıkışın türevi için genelleştirilmiştir. Bu gözlemleyicide türevin derecesinin arttırılmasının gözlemleyici performansını arttırabildiği gösterilmiştir. Örnek sistem olarak bir çeyrek taşıt süspansiyon sistemi ele alınmıştır. Gözlemleyiciler bu sistem için karşılaştırılmıştır ve gözlemleyicilerin gürültü performansı incelenmiştir.In this thesis, the Luenberger observer and the derivative observer, which is generated in this thesis, are given via linear matrix inequalities. It is shown that, the Proportional-Derivative observer given for descriptor systems can't be designed via linear matrix inequalities, but instead that is necessary to use bilinear matrix inequalities. In order to improve estimation performance, the constructed output signal of the observer is omitted from the model for the Luenberger, derivative and Proportional-Derivative observer. Design methods have been presented for the new proportional, derivative and Proportional-Derivative observer models. The new Proportional-Derivative observer from these observers, is generalized as the nth Proportional-Derivative observer for the derivatives of the output. It has been shown that increasing the number of derivatives in this observer can increase the performance of the observer. A quarter car suspension system is considered as an example system. Observers were compared for this system and the noise performance of the observers was examined

Zero/low overshoot conditions based on maximally‐flatness for PID‐type controller design for uncertain systems with time‐delay or zeros

Abstract This paper extends the characteristic ratio approach using novel inequalities to ensure zero/low overshoot for linear‐time‐invariant systems with zeros. The extension provided by this paper is based on the maximally‐flatness property of a transfer function, where the square‐magnitude of the transfer function is ensured to be a low‐pass filter. In order to be able to design low‐order/fixed structure controllers, a partial pole‐assignment approach is used instead of the full pole‐assignment used in the Characteristic Ratio Assignment (CRA) method. The developed inequalities and additional stability conditions are combined into an optimization problem using time domain restrictions when necessary. Although the method given in the paper is general, particular inequalities are developed for PI and PI‐PD controller cases, due to their frequent use in industrial applications. Similarly, First‐Order‐Plus‐Delay‐Time (FOPDT) and Second‐Order‐Plus‐Delay‐Time (SOPDT) systems are considered specifically, since most of the practical systems can be approximated by one of these types. The study is extended to plants with uncertainties where a theorem is developed to decrease computation time dramatically. The benefits of the proposed methods are demonstrated by several examples

Proportional-Derivative Observer Design via BMI Approach using BARON Optimization

National Conference on Electrical, Electronics and Biomedical Engineering (ELECO) -- DEC 01-03, 2016 -- Bursa, TURKEYWOS: 000401519800042This work begins with LMI formulations of Proportional and Derivative observer designs and continues with derivation of the error dynamics of the Proportional-Derivate observer. Proportional observer and Derivative observer are combined to acquire the Proportional-Derivative observer. The observers which are combined can be designed via LMI methods but the new observer can only be designed via BMI formulations. A substitution is used for a term in the error dynamics in order to obtain the BMI formulation of the proposed observer. The performance is optimized via gain minimization, decay rate maximization and L-2 gain minimization. BARON is used to solve the BMI problem to design a PD observer for the given example. BARON is a software that solves nonconvex optimization problems for global optimality via Branch and Bound optimization algorithm. A comparision of three different designs are given to verify that the optimization criteria are valid.Uludag Univ, Muhendislik Fakultesi, Elektrik Elektronik Muhendisligi Bolumu, Istanbul Teknik Univ, Elektrik Elektronik Fakultesi, TMMOB Elektrik Muhendisleri Odasi Bursa Subes

Robust control of railway traction electric drive systems in terms of energy efficiency

In this study, firstly, the model of railway traction electric drive systems is derived analytically along with the indirect vector control approach. In such systems, there are several disturbance and uncertainty sources like varying total weight, weight distribution, environmental conditions, voltage irregularities etc. Furthermore, resistive forces that is based on curve and grade topology, tunnel effects, velocity and aerodynamics of trains directly affects the motion control problem. In order to overcome such difficulties, a new robust pole placement approach is proposed for the speed control of such systems considering the total resistive forces, the possible uncertainties that may occur. The proposed approach is based on affine linear polynomials and D-stability. A conversion is also possible from PID type controllers to PI-PD cascade controller structure in order to eliminate the effects of undesired open loop zeros. Using the proposed approach, it becomes possible to guarantee certain predetermined performance criteria corresponding to a robust performance with energy efficiency. Additionally, correctness and effectiveness of the derived theoretical results are verified via a case study

Luenberger based Observer Design in Time Delay Systems

National Conference on Electrical, Electronics and Biomedical Engineering (ELECO) -- DEC 01-03, 2016 -- Bursa, TURKEYWOS: 000401519800051Observers are necessary to use in case of an urge to control a linear single input-single output system with feedback control or in a necessity to measure states of the system which are not avaliable for measurement or the high cost of the state measurements. Even though simple electrical system states are not effected very much from time delay, the mechanical systems and electrical transmission lines are more effected. To observe the states of a time delay system a time delay observer is necesarry. In this paper we have proposed a new observer for time delay systems via linearizing the delay term in the Laplace domain and we have compared the results with previous observer designs with simulations.Uludag Univ, Muhendislik Fakultesi, Elektrik Elektronik Muhendisligi Bolumu, Istanbul Teknik Univ, Elektrik Elektronik Fakultesi, TMMOB Elektrik Muhendisleri Odasi Bursa Subes