The bang-bang funnel controller

Proc Appl Math and Mech

Trenn

2012

Self Cite

We adjust the newly developed bang-bang funnel controller such that it is more applicable for real world scenarios. The main idea is to introduce a third "neutral" input value to account for the situation when the error is already small enough and no control action is necessary. We present experimental results to illustrate the effectiveness of our new approach in the case of position control of an electrical drive .

“…This makes it necessary to define a new switching logic. However, the new switching logic is very similar to the one in [3]; in particular, all the theoretical results remain valid.…”

Section: Introduction and Controller Designmentioning

confidence: 78%

Section: Introduction and Controller Designmentioning

confidence: 99%

Section: Introduction and Controller Designmentioning

confidence: 99%

See 1 more Smart Citation

The bang‐bang funnel controller: An experimental verification

Proc Appl Math and Mech

Trenn

2012

Self Cite

“…(see (a) and (b)). Asymmetric funnels with upper F + 0 (·) and F − 0 (·) lower boundary, where F + 0 (t) > F − 0 (t) for all t ≥ 0, are possible (but neglected here) [21], [22]. perturbed by bounded measurement noise n m (·) ∈ L ∞ (R ≥0 ; R) evolves within the prescribed funnel (= the set given by…”

Section: A Funnel Control For Relative-degree-one Systemsmentioning

confidence: 99%

Funnel control for speed & position control of electrical drives: A survey

2011 19th Mediterranean Conference on Control &Amp; Automation (MED)

Hofmann

Doncker

et al. 2011

In this survey we introduce a simple high-gain based adaptive controller -the funnel controller -which neither identifies nor estimates the system under control. The proportional funnel controller is applicable for all (nonlinear) systems with relative degree one or two, stable zero-dynamics (e.g. minimum-phase in the linear case) and known sign of the high-frequency gain; hence only structural knowledge is required for controller implementation. The control performance is inherently robust to parameter uncertainties or variations not affecting the system structure. Furthermore, the funnel controller is capable of reference tracking of time-varying command signals with prescribed transient accuracy: the control error is forced to evolve within a prescribed "funnel". Its boundary can be fixed by e.g. a decreasing function of time giving an upper bound on the error transient behavior. Finally, we apply the funnel controller for speed and position control of an (unknown) electrical drive with friction and load disturbances. Measurement results are presented and compared with classical PI/PID control. funnel control, non-identifier (high-gain) based adaptive control, prescribed tracking, prescribed accuracy, robustness.

“…This derivation has several consequences: (i) the bounds help us to understand the interplay between the two different "players" k 0 (·) and k 1 (·); (ii) if the entries of (1.1) are known, it may be possible to determine a sharper number f feas ; (iii) for simplicity we have considered only symmetric funnels, which is a rather hard assumption; this can be relaxed, and the feasibility bound becomes smaller; see [21] for a more detailed analysis in a comparable context.…”

Section: Input Saturationmentioning

confidence: 99%

Funnel Control for Systems with Relative Degree Two

Hopfe

Ilchmann

et al. 2013

SIAM J. Control Optim.

Self Cite

108

Abstract.Tracking of reference signals y ref (·) by the output y(·) of linear (as well as a considerably large class of nonlinear) single-input, single-output systems is considered. The system is assumed to have strict relative degree two with (weakly) stable zero dynamics. The control objective is tracking of the error e = y − y ref and its derivativeė within two prespecified performance funnels, respectively. This is achieved by the so-called funnel controller u(t) = −k 0 (t) 2 e(t) − k 1 (t)ė(t), where the simple proportional error feedback has gain functions k 0 and k 1 designed in such a way to preclude contact of e andė with the funnel boundaries, respectively. The funnel controller also ensures boundedness of all signals. We also show that the same funnel controller (i) is applicable to relative degree one systems, (ii) allows for input constraints provided a feasibility condition (formulated in terms of the system data, the saturation bounds, the funnel data, bounds on the reference signal, and the initial state) holds, (iii) is robust in terms of the gap metric: if a system is sufficiently close to a system with relative degree two, stable zero dynamics, and positive high-frequency gain, but does not necessarily have these properties, then for small initial values the funnel controller also achieves the control objective. Finally, we illustrate the theoretical results by experimental results: the funnel controller is applied to a rotatory mechanical system for position control.