Abstract:
Robust control design for nonlinear systems is one of the most explored topics in recent
literature. Conventionally, techniques like Taylor’s approximation, feedback
linearization, and gain-scheduling are applied on nonlinear system models to find their
simplified linear equivalent models. The system can then be controlled using some linear
control techniques like PD, PI, PID or LQR, etc. The performance of controllers designed
based on linear control techniques is likely to suffer due to external disturbances and
modeling uncertainties. Due to the limitations of linear control techniques, nonlinear
model-based control techniques became the active research area. Among nonlinear
control techniques, Lyapunov-based controllers guarantee robustness to matched and
mismatched uncertainties. Moreover, sliding mode control is the most used Lyapunov
method in nonlinear control because of its robustness to parametric uncertainties and
matched disturbances.
From the control design perspective, settling time is a very important parameter. For
nonlinear systems, the desired settling time is pre-determined only by the use of terminal
sliding mode control. Terminal sliding mode control used a nonlinear sliding surface and
the problem with the terminal sliding mode is the singularity. However, terminal sliding
mode control guarantees the convergence of states to zero after a finite time. In this
thesis, a linear sliding surface is used to design a finite settling time nonlinear controller.
The definition of finite settling time, in the context of this thesis, is the time after which
the outputs of a system remain in the pre-assigned error margin. In the proposed method,
the finite settling time of the system under matched perturbations can be pre-calculated
and the output of the system is guaranteed to remain in a bound for all the time. The
validation of methodology for higher-order single input single output nonlinear systems is
shown by simulations of three practical systems including simple pendulum, solenoid
actuator, and single-link flexible joint robotic manipulator.
