Control of an offshore wind turbine modeled as discrete system
Pedro Varella Barca Guimarães Suzana Moreira Avila
UNIVERSIDADE DE BRASÍLIA - BRAZIL
EO L UnB-UFG
Guide
• Introduction
• Objectives
• Inverted Pendulum Model • Motion’s Equation
• Transfer Function
• Numerical Analysis
• Proportional Control • Block Diagram (Closed-Loop)
• Graphic Result
• Block Diagram (Open-Loop)
• Conclusions
Guide
• Introduction
• Objectives
• Inverted Pendulum Model • Motion’s Equation
• Transfer Function
• Numerical Analysis
• Proportional Control • Block Diagram (Closed-Loop)
• Graphic Result
• Block Diagram (Open-Loop)
• Conclusions
Guide
• Introduction
• Objectives
• Inverted Pendulum Model • Motion’s Equation
• Transfer Function
• Numerical Analysis
• Proportional Control • Block Diagram (Closed-Loop)
• Graphic Result
• Block Diagram (Open-Loop)
• Conclusions
Objectives
• Analise offshore wind turbine’s linear dinamic behavior and stability, modeled as an inverted pendulum;
• Look for a critical situation for its torcional spring to apply a proportional control.
Guide
• Introduction
• Objectives
• Inverted Pendulum Model • Motion’s Equation
• Transfer Function
• Numerical Analysis
• Proportional Control • Block Diagram (Closed-Loop)
• Graphic Result
• Block Diagram (Open-Loop)
• Conclusions
Inverted Pendulum Model
Motion’s Equation
(𝑀 +𝑚𝑏 +𝑚𝑐) (𝑚𝑏 + 2.𝑀). 𝑎
(𝑚𝑏 + 2.𝑀). 𝑎 𝐼 + (𝑚𝑏 + 2.𝑀). 𝑎2𝑢 𝜃
+ 𝑐 00 0
𝑢 𝜃
+ 0 00 𝐾𝑚 − 𝑚𝑏 + 2.𝑀 . 𝑔. 𝑎
𝑢𝜃
=𝐹
2. 𝑎. 𝐹
Inverted Pendulum Model
Transfer Function
• A = (mb + 2.M).a².(mc - M) + (M + mb + mc).I
• B = (I + (mb + 2.M).a²).c
• C = (M + mb + mc).(Km – (mb + 2M).a.g)
• D = (Km – (mb+2M).a.g).c
𝐺 = 𝑠 𝑚𝑏 +𝑚𝑐 . 𝑎 + 2. 𝑐. 𝑎
𝑠3. 𝐴 + 𝑠2. 𝐵 + 𝑠. 𝐶 + 𝐷
Inverted Pendulum Model
Numerical Analysis
Km values Poles
Km = 8,2763.1014 -0,0000 + 840,21i -0,0000 - 840,21i
-0,0000
Km = 8,2763.108 -0.0014 + 0.6997i -0.0014 - 0.6997i
-0.0034
Km = 8,2763.107 0.3805 -0.3832 -0.0034
Guide
• Introduction
• Objectives
• Inverted Pendulum Model • Motion’s Equation
• Transfer Function
• Numerical Analysis
• Proportional Control • Block Diagram (Closed-Loop)
• Graphic Result
• Block Diagram (Open-Loop)
• Conclusions
Proportional Control
Transfer Function
• A = (mb + 2.M).a².(mc - M) + (M + mb + mc).I
• B = (I + (mb + 2.M).a²).c
• C = (M + mb + mc).(Km – (mb + 2M).a.g) + (mb+mc).(mc + mb + M)
• D = (Km – (mb+2M).a.g).c + 2.c.a.(mc + mb + M)
Poles:
• -0,0000 + 0,1656i;
• -0,0000 - 0,1656i;
• -0,0061.
𝐺 = 𝑠 𝑚𝑏 +𝑚𝑐 . 𝑎 + 2. 𝑐. 𝑎
𝑠3. 𝐴 + 𝑠2. 𝐵 + 𝑠. 𝐶 + 𝐷
Guide
• Introduction
• Objectives
• Inverted Pendulum Model • Motion’s Equation
• Transfer Function
• Numerical Analysis
• Proportional Control • Block Diagram (Closed-Loop)
• Graphic Result
• Block Diagram (Open-Loop)
• Conclusions
Conclusions
• The inverted pendulum is a system originally unstable and with a non-linear behavior;
• It was possible to identify a critical situation to apply the proportional control;
• The proportional control was effective for this problem:
• Stabilized the system;
• Kept it within the regime of small displacements.
References
• Ogata, K., Modern Control System, 4ª Edição, Prentice-Hall, New Jersey, 2002
• Pao L.Y. and Johnson K.E., A tutorial on the dynamics and control of wind turbines and wind farms Proceedings of the American Control Conference, St Louis, EUA, 2009
• A. C. Drummond, K. C. Oliveira, A. Bauchspiess, Estudo do Controle de Pêndulo Inverso sobre Carro utilizando Rede Neural de Base Radial, IV Congresso Brasileiro de Redes Neurais, 1999.
• Gordon M. Stewart, Matthew A. Lackner, The effect of actuator dynamics on active structural control of offshore wind turbine, 2011
Top Related