Abstract:
In this thesis we consider a class of nonlinear systems that are underactuated in nature. Un deractuated mechanical systems are those that have fewer degrees of actuation than degrees of
freedom. In particular we proposed a novel approach for controlling underactuated mechani cal systems using robust adaptive controller and dual model-free control framework [18]. The
primary goal of this control framework is to generate stable limit cycle on both actuated and
un-actuated coordinates. A limit cycle is a closed curve in the phase plane of a nonlinear system
that attracts the system’s trajectories over time. It is a common and important phenomenon that
can describe the stable and periodic behavior of many practical systems. A hierarchical control
structure has been used to complete the objective. The high-level controller is being used for
the reference trajectory generation for underactuated joint while keeping the internal dynamics
stable. Then the low-level controller is used for the tracking of the reference trajectories on
the underactuated coordinate. The controller that we have used in this framework was initially
designed for fully actuated systems by Hayat et al. [33]. This controller only uses joints angles,
velocities and their integrals to calculate the control input therefore it also acts as a model free
controller which is not only robust but also optimal and easy to implement. The robustness and
optimality of this controller has already being proved theoretically using ISS and H∞ control
techniques in [31]. This framework will not only completes our goal but also carries the robust ness and stability analysis of the original controller for underactuated system. The proposed
framework outperformed the existing approach in terms of adaption, robustness, and optimality.
The performance and the efficiency of the proposed control approach are validated by the hard ware experiments on the rotary inverted pendulum, vertical take-off and landing aircraft model
and also compared it with another model-free approach (i-PID [23]), along with the simulation
results of cart-pole pendulum and the leg-foot model on deformed ground.
