Describing function

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

Feedback control for oscillations with CPG architecture

Abstract: This paper presents a method for designing a nonlinear feedback controller for a linear plant to achieve an oscillation with a prescribed profile as a projection of a stable limit cycle of the closed-loop system. The controller architecture is based on the central pattern generator, a biological oscillator composed of interconnected neurons that control rhythmic body movements during animal locomotion. The nonlinear control design problem is reduced, approximately, to a linear eigenstructure assignment problem through describing functions and the multivariable harmonic balance method. We then provide a necessary and sufficient condition for existence of a feasible controller assigning a given eigenstructure, as well as a parametrization of all such controllers. A numerical example demonstrates the efficacy of the proposed design method.

Non-linear proportional–integral–derivative synthesis for unstable non-linear systems using describing function inversion with experimental verification:

Abstract: This paper demonstrates a new non-linear proportional–integral–derivative (PID) controller synthesis approach using a describing function inversion technique for unstable systems where a mathematical model may not be available. The approach is applied to an inverted pendulum experimental set-up whose dynamic behaviour is very sensitive to the amplitude level of excitation. The procedure involves stabilization of the unstable system followed by generation of the describing function models of the stabilized closed-loop system. Then, the corresponding unstable open-loop frequency domain models at various operating regimes are extracted. A controller at nominal conditions is designed, followed by obtaining the corresponding desired open-loop frequency domain model. A set of controllers that force the open-loop behaviour of the system mimic, which is desired at various operating regimes, is designed by optimization. Finally, the controller gains are inverted using a describing function inversion technique foll...

Real-time Parameter Estimation of Hydraulic Servo Actuator Systems Using Self-excited Oscillation Method : Online Identification of Approximated Transfer Function Composed of Integral and Second Order Lag Elements

Abstract: The hydraulic servo actuator system is generally dealt with as a second order delay element. The self-excited oscillation method has the advantage that it enables easy estimation of the dynamic parameters of the approximated second order transfer function without valuable measuring instruments such as a FFT analyzer. This study utilizing the self-excited oscillation method suggests the real-time identification algorithm. In order to demonstrate the method's effectiveness, the proposed method was experimentally compared with the frequency response characteristics. Results indicate that both method shows good coincident. It was also confirmed that when the supply pressure and additional torque are continuously changed in the hydraulic system, the damping coefficient and undamped natural frequency were updated on the PC monitor. In addition, amplitude and frequency correction coefficients are analytically obtained from the describing function considering the phase shift, and compared with the simulation results.