The Robust H Control for Inhibition of Load on Offshore Wind Turbines Variable Pitch Control Ping JIANG1,2, SHU-zhen GUO1

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1 3rd International Conference on Machinery, Materials and Information echnology Applications (ICMMIA 25) he Roust H Control for Inhiition of Load on Offshore Wind urines Variale Pitch Control Ping JIANG,2, SHU-zhen GUO College of Electronic and Information Engineering, Heei University, Baoding 7; 2 Heei University-Rockwell Automation Laoratory2, Baoding @qq.com Keywords: wind turines, inhiition of load, H control, variale pitch control, LMI Astract. Offshore wind power industry develop rapidly in recent years. Offshore wind has many advantages compared with onshore wind turine. For example, it do not take up land and can make etter use of the sea wind resources. However, the flexile components of wind turines violent viration will cause the fatigue damage and increase the cost of the maintenance and reduce the service life. Pitch variale is an effective means of control to prevent the sea wind of the interference. In recent years, roust control has won a igger development. In the paper a multi-ojective pitch control strategy ased on roust theory is proposed for large wind turines. he experimental results shows that the roust H control has a good effect on the wind turines variale pitch control.. Introduction Human is facing the prolem of environmental pollution, resources shortage and the ecological deterioration. Wind power industry, especially for offshore, has many advantages such as widely distriuted, renewale, safety, reliaility and so on. herefore, the development of offshore wind power has ecome a gloal trend. However, offshore wind need to overcome more complicated and more severe natural environment conditions. With the improvement of wind power technology, the size and weight of the wind turines growth rapidly. Wind turines need to ear a lot of pressure ecause of its great ody shape. Mechanical parts of the weight increasing will lead to rising costs. Many manufactures lower the system costs y reducing the weight of the wind turines. he decrease of the parts weight often lead to changes in the structure of the wind power properties. It increasing the system flexile. At this time, the wind turine can e regarded as the flexile systems with rigid modal. Meanwhile, the offshore wind turine has long een under a random superposition of wind and ocean wave. It will ring strong dynamic load to the system. he iggest impact on the operation of wind turines is random wind. Study on the suitale control strategies to reduce the dynamic load of offshore wind power is important for us. he aerodynamic force is the main source of the system load. By changing the pitch angle of the lades, wind turines can reduce the aerodynamic loads. For improving the economic enefits of wind turines, we can increase the system reliaility, prolonging the service life. Pitch control is divided into uniform pitch control and independent variale pitch control. Unified pitch control is only valid for alancing the load on its wind turine. But the independent variale pitch control can suppressed unalanced load. In this paper we only study uniform variale pitch control strategy. Uniform pitch control can e grouped into a single target control and mufti-ojective control. Single target only consider speed control / power control, regardless of other factors. However, multi ojective control can consider the other targets, especially for inhiit the viration of machine parts, when adjust the speed / power at the same time. he literature [] sing the sliding mode variale structure control to adjust the pitch, it can suppressed the viration of the tower and lades. he method has a certain degree of roustness. However, it improves the utilization rate of the implementing agencies, osts more energy consumption. He Bossanyi [6-7] installing the acceleration sensors in the top of the tower to prevent viration around the tower, however, his method ignores the tower viration coupling etween the rotor speed. he literature[]application the modern control 25. he authors - Pulished y Atlantis Press 562

2 theory, design the disturance attenuation controller(dac) and linear quadratic regulator(lqr)from linear model of the system. But it ring the speed steady error, what s more, it requires a high precision of the system. he literature[]design a predictive controller to reduce the viration of drive shaft, ut it is a complex method and difficult to realize. Literature[]design a Model - ased adaptive control strategy of dynamic load of the wind wheel,improving the wind turine roustness,unfortunately,it is difficult to realize. Dynamic model of wind turine parameters have large uncertainties.it rings some difficulties to controller design.his paper presents a multi-ojective control strategy which can reduce the load of wind turine. Based on the state feedack theory and linear model of the system, using LMI approach to design a variale pitch controller. In the end of the paper,the simulation results shows that the control strategy can effectively reduce the tower and lade viration and it has good roustness to parameter variations. 2. Model of variale - pitch system he wind turine model was provided y literature[].his article does not consider unalance load ecause the unalancing load can only e carried out y the independent variale pitch control. he unified variale pitch can only control load alance and it response is slowly. his study selects only 3 degrees of freedom, it contains that:the tower viration modes, average mode of lade flapping and generator angle. In this chapter, considering the aove 3 degrees of freedom nonlinear model, so the linear system is written as: q = f ( q, q, u, ud, t) () Where u is the control input(pitch angel), ud disturance input(wind speed);and t is the time. q = ( q, q2, q3), q : the wind turine tower viration modes. q 2 : the Generator angle q 3 :the wind average mode of lade flapping. In high wind ares, the wind turine operating at the rated working point, generator electromagnetic torque remain constant, so the torque is treated as control inputs. We can otain the model under the matching point as: x = a a a a a x u d 3 ud (2) a4 a42 a43 a44 a45 32 d 32 a a a a a d 33 ( x x x x x ) = q q q q q ; is the state change, hat is, the difference etween actual value and the alance point. he mechanism of pitch variale is a huge inertia system.he linear model of pitch actuator can e simplified as a part of first inertia, the model can e descried y: G( s) = (3) τ s + urning it into state - space expression: xτ = x + u (4) τ τ τ τ is the pitch actuator time constant; x a = u ; u is the controller output value. In order to improve the speed regulator performance and eliminate steady state error, we can add the speed of error integrals as the system state variales: 563

3 x e = x4 dt (5) After adding state variales, the model of the system can e written as: x = a3 a32 a33 a34 a35 3 x + u + d 3 ud a4 a42 a43 a44 a45 32 d 32 a5 a52 a53 a54 a55 33 d τ τ x = ( x x x x x x x ) e (6) 3. he H Controller he target of the H control is minimize the output energy. Assume that the generalized plant and controller are time-invariant and finite dimensional model. he most general lock diagram of a control system is shown in fig.. w u G( s) K( s) Fig.. he generalized plant he general plant consists of everything that actuators which generate input to the plant, sensors measuring certain signals, etc. he controller consisted of the engineer s design part. he signals w,z,y and u are, in general, vector-valued functions of time. he components of w are all the exogenous inputs, references, disturances, sensor noises and so on. he z contains all the signals we want to control: tracking errors etween reference signals and plant outputs, etc. he vector y including the outputs of all sensors. Finally,u contains all control inputs to the generalized plant. he system can descried in transfer function as: It also can e written as: G ( s) G = G 2 z y ( s) G2( s) ( s) G ( s) 22 x = Ax + Bw + B2u z = Cx + Dw + D2u (8) y = C2x + D2w + D22u he control ojective is a closed - loop system stale and minimize the impact of interference on the output. he transfer function now can written as: wz = ( G + ) < γ G2K( I G22K) G2 (9) he optimal H control is : min zw ( s) = γ () K he optimal H control prolem is difficult to solve, so we always discuss the prolem of the suoptimal control zw s < () ( ) γ (7) 564

4 Infinite norm of the H transfer function can descrie finite maximum gain of the input energy to the output power.here are many methods to solve H control prolem[2,3]. H control theory can e divided into the frequency domain and time domain method. State Space method, including the method of Riccati equation and LMI. But the Riccati method are often dependent on the adjustment of parameters. And cannot optimize the performance indicator γ.however, the Linear matrix inequality(lmi) approach can overcome the aove shortcomings of the Riccati method. he Matla has een developed LMI oolox.it provides a great help for simulation and design of control system. Based on the Bounded real lemma[2], we can making the transfer function inequality() into linear matrix inequalities, it can e descried as: min ρ AX + B2W + ( AX + B2W ) B ( C X + D2W ) B I D < (2) C X + D2W D ρi X > he state feedack control law is: K = WX H control is a kind of optimal control prolems with state regulators. We can design the feedack control law to enale closed - loop system to stailize and making the transfer function minimum. his feedack is a convex optimization prolem with linear matrix inequalities(lmi) constraints and linear ojective function. By reference[2],the LMI Solver mincx in the oolox can e applied to solve the optimization prolem. 4. Simulation he model data can e found in the literature[]. he linear system s matching point ased on 8m/s wind speed, variale pitch actuator s time constant τ =.2s. Generalized model of the entire system is: x = *.87 x + u +.32 u d Based on this state equation, the lock of state feedack method is shown in fig.2. w u B B 2 + x D 2 s Fig.2. he lock diagram of state feedack method Using mincx function to solve this prolem. LMI is a good way to solve this prolem. With the help of matla software, we can get the results as follows: K=[ ] Control performance is verified y simulation in the whole responses.he results are shown in fig.3-fig.6 A K x C C 2 + z y (2) 565

5 Fig.3. the tower viration displacement Fig.4. the lades viration displacement Fig.5. the torque speed (2r/m) Fig.6. the change of pitch angle By the simulation results,the H controller can make the system stale. As is seen in fig.3, When the tower deviating from the equilirium position.8 meters y the interference wind, It will return to equilirium in 2 seconds. he lades will come ack to the working point in seconds when it out of alance.4 meters. Meanwhile, the torque(fig.5) remains constant. However, it increase the efficiency of the variale pitch actuator(fig.6). 5. Conclusion his paper design a controller to reduced the wind turine load ased on H theory. his control strategy can effectively restrain the viration of tower and lades y increasing the usage of variale pitch. he algorithm has roustness and easy to realize, more importantly, it has a good restraining effect on wind disturance. References []Shuai Xiao Inhiition of large-scale wind turine variale pitch control with Sliding Mode [J] ransactions Of China Electrotechnical Society 23 28(7) [2] Li Yu Roust control linear matrix inequalities Methods(LMI) [M] singhua University Press 22:6-64 [3] J. C. Doyle K. Glover etc. Roust and Optimal Control National Defence Industry Press 22 p5-2 [4] Xia Changliang, Song Zhanfeng. Pitch control of variale speed constant frequency windturines ased on active-disturance-rejection controller [J] Procee- dings of the CSEE, 27, 27(4): [5] Geng Hua, Yang Geng. Output power level control of variale-speed variale-pitch wind generators[j]. Proceedings of the CSEE, 28, 28(5):

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