Adaptive Tracking Control of Linear Uncertain Mechanical Systems in Presence of Unknown Sinusoidal Disturbances
This paper describes the design and implementation of an adaptive disturbance rejection
approach for single-input-single-output (SISO) linear-time-invariant (LTI) uncertain
systems subject to sinusoidal disturbances with unknown amplitude and frequency.
The technique requires the construction of a set of stabilizing tuning functions
utilizing a state estimate observer in a backstepping fashion to achieve
asymptotic disturbance rejection. The tuning functions design is based on a single
Lyapunov function incorporating both the error states and update law, and hence,
global stability and improved transient performance are readily achieved. Utilizing
only the system output, a virtual control input is used in place of non-measurable
and unknown signals. The performance of the adaptation algorithm is demonstrated
through simulations for both regulation and tracking of a single-degree-of-freedom
(SDOF) system with unknown parameters and subject to an unknown sinusoidal disturbance.
The simulation results are verified experimentally on a SDOF mass-spring-damper setup.
Significant matching between the simulation and experimental results is observed.
The extension to multi-degree-of-freedom (MDOF) systems with practical application
to active vibration suppression as well as active noise silencing is currently being studied.
Many mechanical systems are subject to periodic disturbances.
Traditionally, the controller design is influenced by a-prior knowledge
of the disturbance signal to a large extent.
In most cases, the disturbance signals are completely unknown or not
directly measurable, or the system parameters are not known precisely;
hence, the need for a adaptive controller is apparent.