Adaptive Gain PID Control for Mechanical Systems

The design and use of PID controllers is a part of what has been denominated Classical Control, which as the name implies, has been studied for many years (DiStefano et al. 1996), however it continues to be a source for research (Alvarez et al. 2008), (Ang et al. 2008), (Su et al. 2010). The structure of the controller contains a differential term to aid in the reduction of system friction and an integral term to attenuate steady state error. The drawbacks of this control scheme, particularly for nonlinear mechanical systems, include the difficulty in selecting adecuate controller gains, a process usually refered to as tuning. The difficulty usually lies in the fact that if the controller gains are set too small, the control objective may never be reached, whereas the selection of excesively large controller gains may result in system instability. Many approaches have been proposed to properly tune PID gains (Ang et al. 2008), (Chang & Jung 2009), (Su et al. 2010), others have tried to improve upon the performance of the PID controller by including modern control techniques such as neural networks, fuzzy logic or variable structure control (Guerra et al. 2005). Among these, variable structure control, specifically sliding mode control, has shown to possess certain desirable properties, such as disturbance rejection and finite time convergence; however it also presents unwanted behaviors mainly high frequency switching, a phenomenon refered to as chattering, which is undesirable in mechanical systems because it can cause accelerated wear of the mechanical components as well as activate unmodeled dynamics. One solution presented is to include an adaptive gain in the high frequency term so that the desirable properties may be exploited, and the undesirable effects minimized, achieving an enhanced performance (Guerra et al. 2005).