Adaptive compensation strategy for the tracking/rejection of signals with time-varying frequency in digital repetitive control systems

Abstract

Digital repetitive control is a technique which allows to track periodic references and/or reject periodic disturbances. Repetitive controllers are usually designed assuming a fixed frequency for the signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A usual approach to overcome the problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. However, this sampling period adaptation implies parametric changes affecting the closed-loop system behavior, that may compromise the system stability. This article presents a design strategy which allows to compensate for the parametric changes caused by sampling period adjustment. Stability of the digital repetitive controller working under timevarying sampling period is analyzed. Theoretical developments are illustrated with experimental results.

Spatial observer-based repetitive controller: An active disturbance rejection approach

“…(3) Implement a digital system that adjusts the sampling frequency according to the speed changes (Olm, Ramos, & Costa-Castelló, 2010), in order to keep constant the number of samples per period of the disturbance signal. This allows larger frequency changes but involves a more complex stability analysis since the control system is a Linear Time Varying system (Olm, Ramos, & Costa-Castelló, 2011).…”

Precompensated Second Order Repetitive Control of an Active Filter Under Varying Network Frequency

“…Nevertheless, this transforms the original LTI system into an LTV one, thus modifying, or even destabilizing, the closed‐loop system dynamics. Aimed at annihilating the effect of the time‐varying sampling and forcing an output behavior corresponding to that of the nominal sampling period , a precompensator is introduced between the nominal controller G c ( z ) and the plant .…”

“…As an example, the blue line in Fig. shows the first harmonic magnitude response evolution of the modifying sensitivity function against a relative deviation of the real sampling period with respect to the “nominal” , namely where S M o d (·) is defined in using σ =− 1, H ( z ) = 1, G x ( z ) = 1/ T o ( z ), and Notice that even small deviations of entail an important performance reduction for odd‐harmonic RC , a situation which is even worse at higher harmonics. Importantly, this behavior may be alleviated by HORC, as explained in the next subsection.…”

“…This technique, introduced in and validated in a mechatronic plant, is here successfully applied to the shunt active power filter. Notwithstanding, the experimentation in also revealed two other minor, but non negligible, sources of performance decay problems that conventional RC plus the adaptation‐compensation scheme could not address: possible uncertainties in the estimation of the network frequency and innacuracy in the implementation of the sampling time due to quantization limitations. However, high order repetitive control (HORC) is well known to efficiently attenuate small mismatches between actual and implemented values of ratio , where T n and T s stand for the network period and the sampling period of the plant, respectively .…”

Repetitive controller design for testing table systems based on angular position data storage

“…Recently, some new approaches are presented to overcome this drawback in the framework of repetitive control. An idea of changing the sampling period of the digital repetitive controller adaptively is investigated and designed [10]. High-order repetitive control is introduced to Table either improve the robustness for period-time uncertainty or reduce the sensitivity for non-periodic inputs of standard repetitive control schemes [11].…”