Validating Controllers for Internal Stability Utilizing Closed-Loop Data

Abstract

We introduce novel tests utilizing a limited amount of experimental and possibly noisy data obtained with an existing known stabilizing controller connected to an unknown plant for verifying that the introduction of a proposed new controller will stabilize the plant. The tests depend on the assumption that the unknown plant is stabilized by a known controller and that some knowledge of the closed-loop system, such as noisy frequency response data, is available and on the basis of that knowledge, the use of a new controller appears attractive. The desirability of doing this arises in iterative identification and control algorithms, multiple-model adaptive control, and multi-controller adaptive switching. The proposed tests can be used for SISO and/or MIMO linear time-invariant systems.Index Terms-Iterative identification and control, multicontroller adaptive switching, multiple model adaptive control, robust control.

Feedforward/feedback multivariable control design for high speed nanopositioning

“…By using inner-outer factorisation, the proposed design is a special case of the structures discussed in [18], [16] where the set-point is filtered by coprime factors of the plant before being injected into the loop (see Fig. 5 in [18]).…”

“…This paper considers a two degree of freedom control based on a feedforward/feedback combination structure for MIMO coupled nanopositioning stages. The proposed control system is a special case of the class discussed in [16] using coprime factorisation. The target is to increase the bandwidth of the closed loop system while preserving the loop robustness.…”

Verifying stabilizing controllers for performance improvement using closed‐loop data

“…In this section, we shall provide our main results on closed-loop performance verification through experiments on an experimental setting shown in Figure 2, which was initially proposed in [12,19] to test the stability of a new controller. This will be achieved by revealing the fact that all transfer functions in H OEP ,C 1 corresponding to Figure 1 (with C being replaced by C 1 ) can be determined by three transfer functions (which will be defined later) in Figure 2.…”

“…Although many adaptive control schemes indeed utilize the real-time measurement data to evaluate performance of the current and candidate controllers, the available closed-loop signals are most likely subject to noise disturbances, and even with a low noise, they may become inadequate to predict performance in advance [18]. Indeed, there is no indication-at least to the point of verifying user-specific performance requirements-of research attempts to evaluate the closedloop performance (as opposed to just stability, see [19]) before a new controller is inserted. In this paper, which builds on our earlier conference paper [20] that was largely confined to scalar plants and incomplete in a number of aspects, we shall propose novel analysis tools for experimentally verifying the closed-loop performance of a proposed stabilizing controller.…”

“…Section 2 states the problem of interest and reviews definitions and notations from the relevant literature that will be used. Section 3 presents our main results for verifying closed-loop performance on the basis of the proposed experimental setting from [19]. Two examples are provided in Section 4.…”