IJCAS

In this paper, a solution for sliding mode controller gain adaptation is proposed. As is well known, tuning the gains in such a controller is a challenging task since it depends on the bounds of uncertainties and disturbances, which are unknown in most cases. An overestimation of the gains may lead to significant activity of the control input, causing high demands on the actuators and producing the chattering phenomenon. The amplitude of this phenomenon is proportional to the amplitude of the control and can be mitigated by reducing the control gain to the minimal value ensuring convergence. Thus, the gain can be adapted to follow a sufficient value capable of rejecting parameter uncertainties and disturbances. The adaptation methodology presented in this paper is based on PID control scheme where a novel thermodynamic approach to analyze stability in the sense of Lyapunov is presented confirming a class of asymptotic stability. Moreover, some simulation results are provided to validate the effectiveness and reliability of the proposed control schemes. The theoretical significance of this work lies in its potential to establish a foundation for designing a general control equation that bridges the gap between discontinuous and continuous control methods. Moreover, this hybrid control approach holds practical value for control application designers in various industries, including processes that demand chattering-free operation (where the widely used PID control is beneficial), and in processes that require high robustness (where the sliding mode control finds its strength).

Keywords: Adaptive control, chattering-effect, PID control, robust control, sliding mode control.