Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.

Super Twisting-Based Nonlinear Gain Sliding Mode Controller for Position Control of Permanent-Magnet Synchronous Motors

Abstract: This paper proposes a super twisting-based nonlinear gain sliding mode controller (STNGSMC) to achieve the position control of permanent-magnet synchronous motors (PMSMs). Nonlinear gain is developed to improve the position tracking performance of a super twisting sliding mode controller (STSMC). The inclusion of nonlinear gain in the STSMC reduces chattering, and the stability of the closed loop is mathematically proven using the Lyapunov theorem considering load torque. In the proposed method, chattering is analyzed using the describing function method under unmodeled dynamics, such as that corresponding to the quantization effect of the digital sensor, sensor resolution, and pulse-width modulation (PWM) switching noise, in PMSM position control systems. Consequently, the STNGSMC can improve the position tracking performance in steady-state responses. The performance of the proposed method is verified using simulations. The experimental results demonstrate that chattering can be reduced by the STNGSMC, consequently improving the position tracking performance.

Using describing function to analyze wriggling phenomenon of fuzzy control systems

Abstract: In this paper, the describing function of bi-dimensional multi-level relay equivalent model of two-input-single-output fuzzy controller is derived. Based on this function, we analyze the wriggling phenomenon of fuzzy control systems, and qualitatively investigate the effect of fuzzy controller scaling factors on the wriggling amplitude. Simulation result has proved the feasibility and accuracy of the describing function technique in the analysis of fuzzy control systems.

Output excitation via second-order sliding-modes to generate periodic motion for underactuated systems

Abstract: Generation of periodic motion for underactuated manipulator is done through the second-order sliding-mode (SOSM) algorithms, particularly via the twisting algorithm. This study is motivated by the recent results which show that the SOSM algorithm may generate a periodic motion if the relative degree of the plant is higher than two. To obtain the desired amplitude and velocity of oscillations we use the describing function and the locus of a perturbed relay system approach. Performance issue of the controllers is illustrated in a simulation study made for a three-link underactuated robot.

Limit cycles in diesel/controllable pitch propeller propulsion systems using load control

Abstract: Marine diesel/controllable pitch propeller propulsion systems using load control can experience limit cycling or bunting. Simplified fourth-order and eight-order models are developed to study the properties of these control systems. The backlash inherent in mechanical-hydraulic type engine governors is taken as the principal non-linearity in the system. Describing function analysis and digital simulation are used to demonstrate the existence and characteristics of the limit cycles. The numerical example is based upon the characteristics of a 1000 foot Great Lakes bulk carrier with 8000 horsepower per shaft. It is shown that an active load control feature, which couples the pitch control to the engine governor, is a major cause of the limit cycles with 15 to 20 second period observed on these vessels. The describing function analysis with the fourth-order model is effective in predicting the limit cycle existence and period. The sensitivity of the limit cycle characteristics to the system parameters is presented. Results are presented for both describing function analysis and simulation for each model for comparison.

Definition of Nonlinear Reflection Coefficient of a Microwave Device Using Describing Function Formalism (Short Paper)

Abstract: At microwaves, it is necessary to define rigorously the large signal reflection coefficient of a nonlinear device. In this paper, the describing function concept is applied to the power waves incident on, and reflected by, a nonlinear element. This method allows us to define the nonlinear reflection coefficient (NLRC) on the power wave basis. This NRLC is then compared with that defined on the current or voltage basis. Numerical calculations applied to nonlinear elements illustrate the theoretical results.