Bozucu-etki gözleyici tabanlı kontrol yöntemlerinin bir Gimbal üzerinde deneysel karşılaştırılması
Experimental comparison of disturbance observer based control methods on a Gimbal
Yazar: MÜCAHİD RIDVAN KAPLAN
Danışman: DOÇ. DR. ZEKİ YAĞIZ BAYRAKTAROĞLU ; DR. ÖĞR. ÜYESİ BURAK KÜRKÇÜ
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Ana Bilim Dalı / Sistem Dinamiği ve Kontrol Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol = Computer Engineering and Computer Science and Control ; Mekatronik Mühendisliği = Mechatronics Engineering
Dizin: Dinamik kontrol = Dynamic control ; Doğrusal kontrol = Linear control ; Geri beslemeli kontrol = Feedback control ; Motor kontrol = Motor control ; Titreşim kontrolü = Vibration control

Özet:
Bozucu-etki gözleyici tabanlı kontrol (BGTK), kapalı çevrim sistem dinamiklerin, tasarım aşamasında belirlenen nominal sistem cevabına yakınsamasını amaçlar. Literatürde ise benzer amaçlarla türetilen birçok farklı yaklaşım mevcuttur. Bu yaklaşımlar ile harici bozucular ve belirsizliklerin tahmin edilmesi sağlanır. Tahmin edilen bozucular sistemin kontrol sinyaline negatif olarak beslenerek giderilmektedir. Bu çalışmada, tekrar edilebilirlik açısından oluşturulan bir simülasyon ortamında, kayda değer çeşitli BGTK yapılarının karşılaştırılması hedeflenmektedir. Bu amaç için ise, yöntemlerin matematiksel formları uygulanabilirlik açısından yeniden ele alınmıştır. Ayrıca, bu çalışmanın konusu olarak seçilen BGTK yapıları şunlardır: Frekans Uzayı Bozucu-etki Gözleyici Tabanlı Kontrol (FUBGTK), Bozucu-etki Uyum Kontrolünde Bilinmeyen Giriş Gözleyicisi (BUKBGG), Belirsizlik ve Bozucu-etki Tahmincisi (BBT), Eşdeğer Giriş Bozucu-etki Tahmincisi (EGBT), Bozucu-etki/Belirsizlik Tahmincisi Tabanlı Gürbüz Kontrol (BTTGK)'dür.

Literatürdeki mevcut çalışmalarla karşılaştırıldığında, çalışmanın katkısı, önerilen kayda değer yöntemleri, kararlı minimum fazlı tek-giriş tek-çıkışlı (TGTÇ) sistem, kararlı minimum olmayan fazlı TGTÇ sistem, kararsız minimum fazlı TGTÇ sistem ve kararlı çok-giriş-çok-çıkışlı (ÇGÇÇ) sistem üzerinde, uygulanabilirlik ve performans değerlendirme açısından, ölçülebilir ve iyi tanımlı özellikler ile simülasyon ortamında karşılaştırmaktır. Simülasyonlara ek olarak, temel BGTK yöntemleri gerçek bir gimbal sistemine deneysel olarak uygulanmıştır. Literatürde deneysel olarak BGTK yöntemlerinin karşılaştırılma konusu bir eksik olarak dikkat çekmekte ve tez kapsamında yapılan çalışmaların bu eksikliği gidermesi planlanmaktadır. Özellikle teorik olarak iyi sonuç veren sistemlerin deneysel uygulamadaki limitleri ortaya koyulmuş olup, pratik ile ilgilenen mühendislere yöntem seçimi ile ilgili önemli bir bakış açısı kazandırılmıştır. 
Bazı yöntemlerin uygulanamadığı sistemlerde ise, o yöntemin uygulanabildiği değiştirilmiş yapılar üzerinde çalışmalar devam ettirilmiştir.

Çalışmada değerlendirilen yöntemler için tasarlanan kontrol sistemleri, her bir yöntemin önerdiği yaklaşımlar doğrultusunda gerçekleştirilmiştir. Örneğin, bir yöntem durum geri beslemeli kontrol ile başka bir yöntem optimal kontrol yöntemi olan doğrusal karesel regülasyon ile bir diğer yöntem ise gürbüz kontrol teknikleri ile ana kontrol sistem tasarımını önermiştir. Sonuçlar, zaman uzayı ve frekans uzayı analizleri kullanılarak yorumlanmıştır. Giriş bozucu-etki bastırma, duyarlılık, döngü transfer ve tamamlayıcı duyarlılık frekans cevapları analitik bir şekilde yazılarak çıkartılmıştır. Zaman uzayı cevapları ise basamak referans, basamak bozucular ve farklı genlik, faz ve frekanslı sinüzoidal bozucu-etkiler altında incelenmiştir.

Abstract:
With the advances in science and technology, the performance expected from the systems is increasing. It is aimed to regain this performance under uncertainties and disturbances. Therefore, disturbance-observer-based control (DOBC) aims to converge closed-loop system dynamics to the nominal system response determined at the design stage with high performance. In the literature, there are many different approaches derived for similar purposes. With these approaches, external disturbances and uncertainties can be estimated. The basic philosophy of the methods is to eliminate the predicted disturbances and uncertainties by feeding them negatively to the control signal of the system. In particular, the gains obtained in areas such as optimal control, robust control, and nonlinear control were quickly adapted to DOBC. In addition to these and similar control theory areas, the developed DOBC methods have also been successfully theoretical and practical for many different system properties such as linear, non-linear, non-minimum phase systems, time-delayed systems, multi-input-multi-output (MIMO) systems are adapted.

This study aims to compare various noteworthy DOBC structures in a simulation environment created in terms of repeatability. To obtain comparative results and to express the problem definitions given by the pioneers of the methods in an equivalent form, various assumptions compatible with the problem have been expressed. With these assumptions, the same disturbance-effect signals have been converted to be applicable for DOBC methods specified with different state-space representations. For this purpose, the mathematical forms of the methods have been reconsidered in terms of applicability. It is aimed that the disruptive-observer methods will be effective under a certain bandwidth and thus make a fair comparison. In addition, the DOBC structures chosen as the subject of this study are Frequency Domain Disturbance Observer Based Control (FDDOBC), Unknown Input Observer in Disturbance Accommodation Control (UIO in DAC), Uncertainty and Disturbance Estimator (UDE), Equivalent Input Disturbance Estimator (EID), and Disturbance/Uncertainty Estimator Based Robust Control (DUEBRC).

Although the dynamic behavior of physical systems is generally non-linear, the applicability of linearization around the equilibrium point has been verified by many different practical applications. Compared with existing studies in the literature, the contribution of the study is to compare the proposed significant methods on various system types, in terms of applicability and performance evaluation, with measurable and well-defined properties in a simulation environment. These systems are stable minimum phase single-input single-output (SISO) system, stable non-minimum phase SISO system, unstable minimum-phase SISO system, and stable multi-input-multi-output (MIMO) system. In systems where some methods cannot be applied, studies have continued on modified structures where that method can be applied. 

In addition to simulations, basic DOBC methods have been applied experimentally with a real gimbal system. The disturbance signals covering a wide spectrum are applied to the real system with a six-degree-of-freedom motion simulation platform. In the literature, the subject of experimental comparison of DOBC methods draws attention as a deficiency, and it is planned that the studies carried out within the scope of the thesis will eliminate this deficiency. In particular, the limitations of the systems that give good theoretical results in experimental practice have been revealed, and an important perspective on method selection has been given to engineers who are interested in the practice. In the application areas with similar system structures, the design difficulties that the researchers interested in the subject may encounter are given in the comparative design steps. 

As can be understood from the specified scope, design criteria may vary with a real or physical system. Bandwidth, speed and interference suppression functions draw attention as the performance metrics that will guide the basic designers the most, and the necessary adaptations can be adjusted directly by determining these variables during the design phase. However, it should be noted that the mentioned metrics cannot be determined arbitrarily in experimental systems and therefore these designs must be evaluated iteratively during the design process for physical systems. The basic steps to be followed for the process are explained in detail on the gimbal example within the scope of the thesis. The source of the disturbances that adversely affect the performance of the gimbal system is clearly known in practical applications. From the platform on which the gimbal system is integrated, a total of six axes of vibration come from three axes of linear acceleration and three of rotational velocity. Linear acceleration data is entered through the system disturbance channel as rotational torque with the mass imbalance of the system. Linear accelerations are reflected to the system by the bending effect, and together with the rotational speeds, they affect the gimbal friction as a disturbance torque.

The results obtained in practical applications are valid for the gimbal system, which is an inertial-stabilized platform. In a different system, these performance criteria may vary. Although the nominal system is highly similar to the real system, very high bandwidth cannot be provided due to parts of the physical system that cannot be modeled. The design in the simulation environment should be evaluated by considering the physical limitations of the real system so that there is no stability difference between simulation and reality. The process is continued by modeling the model uncertainties and updating the design retrospectively, solving the problems that may be encountered in reality and minimizing the differences between simulation and reality. 

The control systems designed for the methods evaluated in the study were carried out in line with the approaches suggested by each method. For example, one method suggested state feedback control, another method suggested optimal control method, linear-square regulation, and another method suggested a main control system design with robust control techniques. To be fair in making this comparison, control system parameters should be chosen on the same criteria (bandwidth). This criterion was chosen based on the settling time parameter via the time-domain system response. Lowering the settling time will increase the system bandwidth. Gradient descent optimization technique was used to minimize the settling time of the system with various control algorithms. The results were interpreted using time-domain and frequency-domain analyses. Input disturbance rejection, complementary sensitivity, loop transfer, and sensitivity frequency responses are written and extracted analytically. Time domain responses are studied under step reference, step disturbances, and sine signals with different amplitudes, frequencies, and phases.