As one of the robust control strategies, Variable Structure Control (VSC) or Sliding Mode Control (SMC) has been widely applied in dealing with norm-bounded system uncertainties for nonlinear uncertain systems. In SMC, the controller is designed such that the uncertain system can reach the desired sliding surface in finite time and can remain on the surface for all the subsequent time. The main contributions of this thesis are to develop new sliding mode control schemes for different control objects. Consequently, the proposed approaches widen the application range to real systems, such as servomechanisms and robotic manipulators, and achieve better control system performance under various control environments.

In the first part of the thesis, five different sliding mode control schemes are proposed.

1. A sliding mode controller with the closed-loop filtering architecture is proposed for a class of nonlinear systems. In the new control approach, the equivalent control profile, which will drive the system to move along the pre-specified switching surface, is acquired by incorporating two first order filters in a closed-loop manner. As a result of the closed-loop filtering and according to the internal model principle, the switching control gain can be significantly scaled down and as a result chattering can be reduced.
2. Two main robust control strategies, sliding mode control and nonlinear H∞ control, are integrated to function in a complementary manner for tracking control tasks. The new control method is designed for a class of nonlinear uncertain systems with two cascaded subsystems. Through solving a Hamilton-Jacobien inequality, the nonlinear H∞ control law for the first subsystem well defines a nonlinear switching surface. By virtue of nonlinear H∞ control, the resulting sliding manifold in the sliding phase possesses the desired L2 gain property and to certain extend the optimality. Associated with the new switching surface, the SMC is applied to the second subsystem to accomplish the tracking task, and ensure the L2 gain robustness in the reaching phase.
3. An integral sliding mode control is analyzed and designed under the framework of Lyapunov technology. A nonlinear integral-type sliding surface is used to yield a sliding manifold specified in the entire state space and two types of unmatched system uncertainties are considered and their effects to the sliding manifold are explored. In the sequel a nonlinear nominal control scheme is proposed to improve the performance of the sliding manifold.
4. A new adaptive variable structure control (VSC) scheme is proposed for nonlinear systems without a prior knowledge of control directions. By incorporating a Nussbaum-type function, the new adaptive VSC law can ensure asymptotic convergence of the tracking error in the existence of non-parametric uncertainties.
5. A new fractional interpolation based smoothing scheme is proposed for variable structure control. Compared with the conventional fractional interpolation scheme, the new scheme achieves the designated tracking precision bound with an adequate and yet moderate gain. Compared with the well known saturation scheme, the new scheme achieves a smoother control profile, and possesses one extra degree of freedom in adjusting the equivalent control gain while retaining the same precision bound. In the new scheme, the equivalent gain nearby the vicinity of the equilibrium can be adjusted to vary from the saturation type to the signum type.

In the second part of the thesis, the issues on the applications of sliding mode control to multi-link robotic manipulators, permanent magnet synchronous motors (PMSM), DC servo motors and parameter identification are further considered.

1. In the first application, a gain shaped sliding mode control scheme is successfully applied for the tracking control tasks of multi-link robotic manipulators. Two classes of low-pass filters are introduced to work concurrently for the purpose of acquiring equivalent control, reducing the switching gain effectively and in the sequel reducing chattering.
2. In the second application, a modular control approach with a gain shaped sliding mode observer is applied to PMSM speed control to minimize the torque pulsations. By virtue of incorporating internal model, the ILC module in the proposed control scheme achieves the desirable feedforward compensation for all torque harmonics with unknown magnitudes. A novel torque estimation module using gain shaped sliding mode observer is further developed to facilitate the implementation of torque learning control.
3. In the third application, via describing function techniques, sliding mode control of DC servo mechanisms is analyzed in the presence of unmodeled dynamics. Based on the analysis of the limit cycle problem, the fractional interpolation based smoothing scheme is then proposed to eliminate the limit cycle, and maintain a reasonable tracking precision bound.
4. Furthermore, an identification scheme suitable for time-varying parameters is developed based on variable structure system theory and sliding mode. The new closed-loop identification scheme addresses several key issues in system identification simultaneously:​ unstable process, highly nonlinear and uncertain dynamics, fast time-varying parameters and rational nonlinear in the parametric space.