Quantitative Feedback Theory and Sliding Mode Control

Abstract

A robust control method that combines Sliding Mode Control (SMC) and Quantitative Feedback Theory (QFT) is introduced in this chapter. The utility of SMC schemes in robust tracking of nonlinear mechanical systems, although established through a body of published results in the area of robotics, has important issues related to implementation and chattering behavior that remain unresolved. Implementation of QFT during the sliding phase of a SMC controller not only eliminates chatter but also achieves vibration isolation. In addition, QFT does not diminish the robustness characteristics of the SMC because it is known to tolerate large parametric and phase information uncertainties. As an example, a driver’s seat of a heavy truck will be used to show the basic theoretical approach in implementing the combined SMC and QFT controllers through modeling and numerical simulation. The SMC is used to track the trajectory of the desired motion of the driver’s seat. When the system enters into sliding regime, chattering occurs due to switching delays as well as systems vibrations. The chattering is eliminated with the introduction of QFT inside the boundary layer to ensure smooth tracking. Furthermore, this chapter will illustrate that using SMC alone requires higher actuator forces for tracking than using both control schemes together. Also, it will be illustrated that the presence of uncertainties and unmodeled high frequency dynamics can largely be ignored with the use of QFT.