No abstract

The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e. stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T–S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T–S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

In this paper, a control system for a mobile four-wheeled robot is designed, whose task is to create stability and achieve proper performance in the execution of commands. Due to the nonlinear and time-varying dynamics, structural and parametric uncertainties of this robot, various control approaches are used in order to achieve stability, proper performance and minimize the effect of uncertainties and modeling errors, etc. The purpose of the control here is to follow a predetermined trajectory by adjusting linear and angular velocities in the presence of external disturbances and parametric uncertainty.In previous articles, the upper band of uncertainties has been assumed known. In this paper, and given that in practice, in many cases it is not possible to know the extent of uncertainties and disturbances in robotic systems, we have assumed that this upper band is unknown. Therefore, the sliding mode control law designed in the paper has been generalized and proved its stability so that by adding an adaptive part to the controller and converting it into a robust-adaptive sliding mode control, the upper band uncertainties are estimated online using these adaptive laws. The results of this typology are expressed in a separate theorem and proved to be stable. The results of simulation with MATLAB software show that the proposed controller ensures optimal performance under external disturbances and parametric uncertainty with less fluctuations.