Prescribed-Performance-Based Sliding Mode Control for Piezoelectric Actuator Systems

A prescribed-performance-based sliding mode control method with feed-forward inverse compensation is proposed in this study to improve the micropositioning accuracy and convergence speed of a piezoelectric actuator (PEA). Firstly, the piezo-actuated micropositioning system is described by a Hammerstein structure model, and an inverse Prandtl–Ishlinskii (PI) model was employed to compensate for its hysteresis characteristics. Then, considering modelling errors, inverse compensation errors, and external disturbances, a new prescribed performance function (PPF) with an exponential dynamic decay rate was developed to describe the constrained region of the errors. We then transformed the error into an unconstrained form by constructing a monotonic function, and the sliding variables were obtained by using the transformation error. Based on this, a sliding mode controller with a prescribed performance function (SMC-PPF) was designed to improve the control accuracy of PEAs. Furthermore, we demonstrated that the error can converge to the constrained region and the sliding variables are stable within the switching band. Finally, experiments were conducted to verify the speed and accuracy of the controller. The step-response experiment results indicated that the time taken for SMC-PPC to enter the error window was 8.1 and 2.2 ms faster than that of sliding mode control (SMC) and PID, respectively. The ability of SMC-PPF to improve accuracy was verified using four different reference inputs. These results showed that, for these different inputs, the root mean square error of the SMC-PPF was reduced by over $39.6\%$ and $52.5\%$, compared with the SMC and PID, respectively.