Closed-Loop Sensitivity Identification for Cross-Directional Systems

TL;DR

The paper tackles the challenge of estimating the closed-loop sensitivity $S(s)$ of fast orbit feedback in a cross-directional, ill-conditioned system where direct disturbance measurements are unavailable. It proposes a modal-space reference signal that decouples the MIMO plant into mode-wise SISO channels, enabling nonparametric estimation of the complementary sensitivity $T(s)$ using Blackman–Tukey analysis. Key contributions include derivation of lower and upper bounds on the reference amplitude to bound estimation error and actuator saturation, and a practical Diamond Light Source case study showing feasibility and limitations for higher-order modes. The approach scales to large cross-directional systems and provides a fault-detection signal, with potential applications in other process industries featuring strong directional coupling.

Abstract

At Diamond Light Source, the UK's national synchrotron facility, electron beam disturbances are attenuated by the fast orbit feedback (FOFB), which controls a cross-directional (CD) system with hundreds of inputs and outputs. Due to the inability to measure the disturbances in real-time, the closed-loop sensitivity of the FOFB can only be evaluated indirectly, making it difficult to compare FOFB algorithms and detect faults. Existing methods rely on comparing open-loop with closed-loop measurements, but they are prone to instabilities and actuator saturation because of the system's strong directionality. Here, we introduce a reference signal to estimate the complementary sensitivity in closed loop. By decoupling the system into sets of single-input, single-output (SISO) systems, the reference signal is designed mode-by-mode, accommodating the system's strong directionality. Additionally, a lower bound on the reference amplitude is derived to limit the estimation error in the presence of disturbances and measurement noise. This method enables the use of SISO system identification techniques, making it suitable for large-scale systems. It not only facilitates performance estimation of ill-conditioned CD systems in closed-loop but also provides a signal for fault detection. The potential applications of this approach extend to other CD systems, such as papermaking, steel rolling, or battery manufacturing processes.

Figures (6)

• Figure 1: Controller structure with plant $P(s)$, plant model $\hat{P}(s)$, IMC filter $Q(s)$, compensator $\Gamma$, disturbance $d(s)$, noise $n(s)$, and reference signal $r(s)$.
• Figure 2: Minimum and maximum sensitivity gains.
• Figure 3: Spectral density of output in modal space.
• Figure 4: Lower (dashed) and upper bounds on the reference amplitude for $u_\text{max}=1\A$, $y_\text{max}=150µm$, and $\epsilon_\text{max}=0.1$.
• Figure 5: Complementary sensitivities and estimation error over modes and frequencies. For each mode, the normalised frequency ranges from 0 to $\tilde{\omega}_i$.