Design of an Optimal Controller for the Roll Stabilization of Surface Ships with Active Fins

Original Research (AR) Received: 09 April 2018 Arslan / JEMS, 2018; 6(4): 291-305 DOI ID: 10.5505/jems.2018.50570 Accepted: 17 July 2018 Journal of ETA Maritime Science J EMS OURNAL Corresponding Author: M. Selçuk ARSLAN Design of an Optimal Controller for the Roll Stabilization of Surface Ships with Active Fins M. Selçuk ARSLAN Yıldız Technical University, Department of Mechatronics Engineering, Turkey ; ORCID ID: https://orcid.org/0000-0002-6853-4522 Abstract In this paper, an optimal controller is designed to control the undesired roll motion of a ship under the effect of sea waves by using active fin stabilizers. The roll dynamics is described by a single-degree-offreedom nonlinear model. An actuator dynamics is also included to the dynamic system. Sinusoidal and random wave models are used to describe the wave elevation that causes disturbance moments in the ship. A worst-case scenario is the application of the periodic wave to bring the ship resonance, whereas the random waves are used to test the system at the smooth and moderate sea states. In designing the controller, the energy optimal control method, which allows both the closed-loop and real-time control of dynamic systems, is employed, and the control law is obtained analytically. The performance of the controller, under the effect of environmental disturbances, is tested by computer simulations and the results are compared with those from LQR controlled ship. Keywords: Ship roll motion, Fin stabilizer, Optimal control, Roll damping. Gemilerin Aktif Kanatla Yalpa Stabilizasyonu için Bir Optimal Kontrolcü Tasarımı Öz Bu çalışmada, dalga etkisi nedeniyle istenmeyen yalpa hareketi yapan bir geminin aktif kanat dengeleme sistemi vasıtasıyla kontrolü için bir optimal kontrolcü tasarımı yapılmıştır. Tek serbestlik derecesine sahip doğrusal olmayan bir model kullanılarak yalpa dinamiği tanımlanmıştır. Ayrıca, kanatlara ait aktüatör modeli de sisteme eklenmiştir. Gemiye bozucu etki yapan deniz dalgalarının modellenmesinde, dalga yüksekliğinin sinüzoidal bir fonksiyon ve rastgele dalga modeli kullanılmasıyla iki yaklaşım benimsenmiştir. Periyodik dalga ile geminin doğal frekansında rezonansa getirilmesiyle olabilecek en kötü durum test edilmeye çalışılırken, küçük ve orta dalgalı deniz durumlarına karşılık gelen iki ayrı rastgele dalga modeli ile gerçekte karşılaşılabilecek durumlar test edilmeye çalışılmıştır. Kontrolcü tasarımında, dinamik sistemlerin gerçek zamanlı ve kapalı çevrim kontrolüne imkan veren enerji optimal kontrol metodu kullanılmıştır. Analitik olarak elde edilen kontrol kuralı vasıtasıyla, bahsedilen bozucu etkiler altında, kontrol performansı bilgisayar simülasyonları ile test edilerek istenmeyen yalpa hareketinin azaltıldığı gösterilmiştir ve bir LQR kontrolcü ile kontrol edilmiş geminin yalpa hareketleriyle karşılaştırılmıştır. Anahtar Kelimeler: Gemi Yalpa Hareketi, Kanat Dengeleyici, Optimal Kontrol, Yalpa Sönümleme. To cite this article: Arslan, M. S. (2018). Design of an Optimal Controller for the Roll Stabilization of Surface Ships with Active Fins. Journal of ETA Maritime Science, 6(4), 291-305. To link to this article: https://dx.doi.org/10.5505/jems.2018.50570 291 © UCTEA The Chamber of Marine Engineers 1. Introduction The ship roll motion caused by wave disturbances might affect the passengers, crews, equipment and cargos adversely. In reducing the undesired roll motion of ships, hydraulically actuated fin stabilizers are widely used. Compared to other roll stabilization techniques, which are rudder roll stabilization, bilge keels, gyrostabilizers, and anti-rolling tanks, active fin stabilizers have higher performance [1]-[3]. Another advantage is that they do not need sophisticated control systems. Therefore, the ship roll stabilization through active fin stabilizers is a widely studied approach. The challenges in the control of ship roll motion have attracted the attention of researchers. For the roll stabilization of a ship through active fins, the design of a classical controller and an adaptive linear quadratic compensator are reported in [4]. In the gain scheduling adaptive controller, which revealed a superior performance than the classical controller, the gains of the regulator are calculated by a multilayer perceptron neural network. For three different sea conditions, the reduction in the roll motion is exhibited. This is one of the few studies using an optimal control method in the field, since optimal control methods have not been widely applied in the control of ship roll motion. Karakas et al. designed a roll motion control system by using the Lyapunov's direct method [5]. The effectiveness of the controller under the effect of beam seas was shown in a simulation study. In [6], the designed proportional, derivative, second derivative controller was tuned by particle swarm optimization algorithms. In simulations and real-time full-scale sea trials, the control algorithm achieved to damp the roll motion significantly. Another method for the ship roll stabilization is proposed in [7], where the fin control design method is based on an adaptive neural-network. In this approach, the disturbance is estimated and Journal of ETA Maritime Science compensated to improve the robustness. The simulation results show that the rolling motion reduced for a ship under the effect of a sinusoidal disturbance. In a recent study [8], the uncertainties in the ship and fin system are identified by a neural network and an adaptive robust fin controller was designed. Another study [9] employing an artificial intelligence technique in the roll stabilization reports the identification of a fishing boat for the roll dynamics and use of a fuzzy logic controller. In a comparative study, it was shown that the fuzzy logic controller handles the nonlinear effects and the time-varying parameters better than the PID controller does. In a recent study, Demirel and Alarçin have designed LMIbased H2 and H∞ state-feedback controllers for the roll reduction of a fishing boat. The results show that both controllers are effective in the roll stabilization and H∞ controller's performance is better [10]. Another recent study discussing the roll reduction for a trawler type fishing boat has proposed the use of a backstepping controller. The results indicate that the roll stabilization by the backstepping controller is highly satisfactory [11]. One of the difficulties in the ship roll motion control is the transport delay due to the hydraulic actuator system. In this direction, a ship roll stabilization system based on a variable structure robust control of fins proposed in [12]. By considering the active anti-rolling fin stabilizer as a mismatching uncertain system, a variable structure robust controller is designed. It is shown that the stability of the closed loop is not affected by the time constant of the actuator. Another difficulty arises from the unsteady hydrodynamic characteristics of the (...truncated)