Development of CRONE reset control

In high-tech industry (sub)nanometre precision motion control is essential. For example wafer scanners, used for production of integrated circuits, have to provide (sub)nanometre precision positioning whilst satisfying challenging requirements on speed at the same time. It is in demanding cases like this that different requirements begin to conflict with each other. A fundamental trade-off between robustness and performance exists as an inevitable result of the waterbed effect in linear control. PID controllers, which have been an industry-standard for many years, do not satisfy the ever increasing demands. In this MSc thesis a novel reset control synthesis method is proposed: CRONE reset control, which combines a robust fractional CRONE controller (Commande Robuste d’Ordre Non-Entier) with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved against gain deviations by creation of constant phase behaviour around bandwidth with the use of fractional operators. The use of fractional operators also introduces more freedom in shaping the open- loop frequency response, allowing fractional factors in Bode’s gain-phase relation. However, waterbed effect remains, which motivates introduction of non-linear reset control in the CRONE design. In reset control, controller states are reset when the error between output- and reference- signal is zero. In frequency domain, using describing function analysis it is predicted that reset filters generate less phase lag for similar gain behaviour. For instance, a reset integrator gives a phase lag of about 38 degrees, which is 52 degrees less compared to the linear integrator. This allows for relief from Bode’s gain-phase relation, breaking aforementioned trade-offs. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. New design rules for CRONE reset control have been developed in this thesis. Three different reset control strategies have been investigated: integrator reset, lag reset and lead- lag/lag-lead reset. For these controllers, a two-degree-of-freedom non-linearity tuning CRONE reset control structure has been developed. This control structure has been implemented digitally within a MATLAB/Simulink environment on a Lorentz-actuated (dual) precision stage via a real-time dSPACE DS1103 controller interface. For the implemented controllers sufficient quadratic stability has been shown using the Hβ-condition. It has been shown that simulated frequency responses using describing function correspond well to experimental identified frequency responses. Moreover, frequency domain measurements have shown that better performance for CRONE reset control can be achieved for same phase margin compared to linear CRONE. Relief from both waterbed effect and Bode’s gain-phase relation has been accomplished. Furthermore, for the same bandwidth, average noise reduction between 1.79dB and 3.93dB has been attained at a number of distinct frequencies above bandwidth. In the fine stage separately and also in dual stage configuration, tracking of a fourth-order input-shaped reference signal (with second-order- and fourth-order feedforward respectively) showed improvement in CRONE reset control compared to linear CRONE. In the dual stage configuration, after decoupling fine stage and coarse stage, tracking performance of a linear CRONE controller has been compared to a CRONE reset controller. In both cases the same linear CRONE-2 controller with a bandwidth of 80 Hz and phase margin of 50° was applied to the coarse stage. On the fine stage a CRONE-1 lag-lead controller was applied with a bandwidth of 150 Hz and a phase margin of 55°. RMS error for a triangular scanning wave with maximal acceleration of 0.25 m/s2 and maximal velocity of 75 mm/s over a stroke of 2 cm, was reduced from 929.8 nm to 443.7 nm.