In the wind turbine manufacturing industry, the bolt-nut joint tightening process is one of the core processes in the full production chain and concerned with assembling the hub body, the pitch system and the bearing unit. This operation is currently executed manually with the aid of different tools and gauges; the main disadvantages are a relatively high degree of variability and the necessity to repeat this task several times during a production run to achieve a satisfactory, final tightening torque within a specified angle range. Moreover, the bolt tightening process includes various uncertainties such as the presence of friction forces and the use of different bolt sizes with different stiffness values which make it highly nonlinear and uncertain resulting in a challenging control problem. To facilitate the development of an effective control strategy, we study the bolt tightening process and propose 4 tightening stages, namely, bolt-nut alignment, partial and full engagement and final bolt tightening. Based on the characteristics of each stage, a fuzzy controller is designed for each stage to realize the respective control objectives. A fuzzy error detector incorporating the knowledge of each stage is proposed for early error detection, making use of the input from a torque and encoder (angular position) sensor. Errors can be detected in each stage to interrupt the process and prevent any damage to the system.

Stability analysis of polynomial fuzzy model-based (PFMB) control systems under the parallel distributed compensation (PDC) design technique is investigated. A new polynomial fuzzy controller (PFC) is introduced to release conservativeness in the existing approaches. Compared to the conventional (PFC), the controller under consideration in this paper has a favorable property which introduces some more variables in the stability conditions such that, the solution of the derived stability conditions can be explored in a larger group of potential solutions. This property may lead to further relax stability conditions. However, the stability conditions will not be in the form of SOS conditions. Hence, particle swarm optimization (PSO) is employed to explore the solution of the derived stability conditions which are in the form of state-dependent BMI. It is shown that the conventional PFC is a special case of that of proposed one. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.