Widespread Application and Limitations of Self-Tuning Controllers in Practice

Self-tuning controllers are increasingly adopted in practical applications today. However, they exhibit certain limitations, particularly in systems with varying orders, time delays, and parameters. To enhance their effectiveness in real-world scenarios, it is essential to develop controllers with stronger robustness. The implementation often involves adaptive algorithms that continuously update controller parameters based on real-time system identification, such as using autoregressive models with exogenous inputs (ARX) for dynamic parameter tracking.

The generalized predictive control (GPC) self-tuning controller, introduced by Clark et al., is a predictive control algorithm grounded in parametric models. It utilizes a receding horizon optimization performance index and combines system identification with self-tuning techniques to mitigate the drawbacks of conventional self-tuning control, thereby achieving enhanced robustness. Algorithmically, GPC solves a quadratic optimization problem to compute control sequences over a prediction horizon, incorporating constraints handling for practical deployment. The emergence of this controller provides new methodologies and perspectives for the evolution of self-tuning controllers in practical applications, offering expanded options and possibilities for robust control solutions. Code implementation typically involves solving Diophantine equations for step-response coefficients and applying cost function minimization with weighting matrices for control effort and output error.