A simple nonlinear scheme for controlling a second-order rate-type servomotor is described. This scheme is referred to as “bang-bang” control since the input to the servomotor is made to “bang” from its maximum value in one direction to its maximum value in the other direction depending only on the sign of an error signal. This bang-bang system oscillates in a continuous high-frequency, low-amplitude limit cycle. The nature of this limit cycle is studied by the describing function approximation and by an exact method. The step and frequency response characteristics of the bang-bang system are discussed and compared with the characteristics of a simple linear system. It is shown that many aspects of the behavior of the bang-bang system can be predicted from rather simple considerations.
Algebraic expressions are given for some critical jump-resonance curves in feedback systems containing one nonlinearity. The usual describing-function approximation is employed, and the following nonlinearities are considered: a) linear plus (2n + 1)th power, b) saturation with hysteresis, c) dead zone, d) backlash.
Abstract
This paper presents describing function analysis and control solution for a friction related problem encountered during the development of a voice coil actuated direct drive for use in turning of automotive camshafts. It is observed that the addition of a high accuracy tracking (repetitive) controller results in a system that is susceptible to limit cycle oscillations induced by Coulomb friction. A local acceleration feedback loop is utilized to shape the system response to disturbance forces and is shown to improve the drive stiffness and prevent performance deterioration due to friction.
Fractional describing function of systems with Coulomb friction