# Load Prediction Control Study of a Pitch Control System for Large Offshore Wind Turbines
## 2 Pitch System Principles and Modeling  
The electro-hydraulic servo pump-controlled variable pitch hydraulic system studied in this paper is illustrated in Figure 1. The system primarily consists of permanent magnet synchronous servomotors, bidirectional fixed-displacement hydraulic pumps, asymmetric hydraulic cylinders, accumulators, directional valves, check valves, and relief valves. By regulating the servomotor's rotational speed, the hydraulic pump's output flow is controlled, thereby adjusting the displacement of the hydraulic cylinder. The piston of the hydraulic cylinder is connected to the blade root via a pitch mechanism, which converts the piston's linear motion into rotary motion to achieve blade pitch adjustment. In the closed pump control system used, the hydraulic cylinder body is fixed on the hub through the hinge, the piston of the hydraulic cylinder is connected with the root of the blade through the hinge, the two hydraulic cylinders are mechanically synchronized, and the pitch action can be achieved by controlling the extension or  
Figure 1: Schematic of electro-hydraulic servo pump-controlled independent variable pitch system. rod. The hydraulic cylinder extends in the direction of the propeller, and the pitch angle increases, while the hydraulic cylinder retracts in the direction of the counter-propeller, and the pitch angle decreases. The principle of the pitch system mechanism is shown in Figure 1(a); by adjusting the flow rate of the output of the motor pump unit to control the hydraulic cylinder operating speed, the pitch speed is controlled. In Figure 1(b) [11], \(\alpha\) is the mounting angle, \(\beta\) is the pitch angle, \(O_{A}\) denotes the articulation point between the hydraulic cylinder body and the hub, \(O_{B}\) represents the rotational axis of the blade, and \(O_{C}\) marks the articulation point connecting the hydraulic cylinder piston and the blade. The distance between \(O_{A}\) and \(O_{C}\) equals the sum of the minimum hydraulic cylinder length (\(L\)) when fully retracted and its displacement (\(x_{p}\)). Meanwhile, the distance between \(O_{B}\) and \(O_{C}\) is a fixed value \(Re\). The distance between \(O_{A}\) and the blade's rotational axis (\(O_{B}\)) is defined as H, which corresponds to the mounting angle. The pitch angle is determined by the geometric relationship between these parameters. Under the assumption of rigid-body behavior for the hydraulic cylinder assembly (including piston rod and linkages), the kinematic relationship between the actuator stroke and the blade pitch angle in the pitch adjustment mechanism (Figure 2) is governed by the following equation:  
\[\beta=\arccos\left[\frac{R_{e}^{2}+H^{2}-(L+x_{p})^{2}}{2R_{e}H}\right]-\alpha, \tag{1}\]  
From Equation (1), it can be concluded that the pitch angle depends solely on the hydraulic cylinder displacement once the pitch mechanism is rigidly installed. Therefore, precise control of the hydraulic cylinder displacement is the primary requirement for pitch angle regulation. Upon receiving the target pitch angle signal from the pitch system, this signal is converted into a hydraulic cylinder position command. The hydraulic cylinder position controller then compares the actual position with the target command and generates a servo motor speed signal. The servo motor drives the hydraulic pump to adjust the flow rate, enabling the hydraulic cylinder to reach the target position. Subsequently, the hydraulic cylinder actuates the pitch mechanism to achieve the desired pitch angle. This completes the pitch angle control process, as illustrated in Figure 3.  
Figure 2: Schematic and principle of variable pitch mechanism. In response to the rapid load fluctuations imposed on offshore wind turbines, the interrelationships between servomotor speed, hydraulic cylinder displacement, and external load disturbances are systematically analyzed in the subsequent sections [12].