Tuning of Proportional Retarded Controllers: Theory and Experiments

Villafuerte, R.; Mondié, Sabine; Garrido, R.

doi:10.1109/tcst.2012.2195664

Cited by 82 publications

(69 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…, ∞. In [16], the parameter space ( , , ) of control law [13] to -stabilize system [12] is determined.…”

Section: A Pr Controller For a Second-order Plantmentioning

confidence: 99%

“…It is well known that noise, time delays, sampling, and unmodeled dynamics deteriorate the performance of such estimators. Hence, it is of relevance to understand the effect of time delays in measurements as well as the potential of such delays as a second degree of freedom for control design (see [16,17]). For this aim, a PR controller design will be presented together with the Mikhailov stability approach.…”

Section: Introductionmentioning

confidence: 99%

“…The analysis of time delays in control systems is not a new topic; particularly, the addition of time delays in the control design has been studied for many years (see, e.g., [18][19][20][21][22][23][24][25][26][27]). In particular, the introduction of time delays in the control law avoids the use of techniques for estimating the derivative action, which is not an easy task under the presence of noise and delays in measurements and increases the cost and complexity of the overall controller design and tuning of the gains [16]. On the other hand, the implementation of a retarded control law requires only memory registers and is relatively simple to program, since it is based on a sum of a proportional signal and the corresponding delayed one.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Proportional Retarded Controller to Stabilize Underactuated Systems with Measurement Delays: Furuta Pendulum Case Study

Ortega-Montiel

Villafuerte-Segura

Vázquez³

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The design and tuning of a simple feedback strategy with delay to stabilize a class of underactuated mechanical systems with dead time are presented. A linear time-invariant (LTI) model with time delay of fourth order and a Proportional Retarded (PR) controller are considered. The PR controller is shown as an appealing alternative to the application of observer-based controllers. This paper gives a step forward to obtain a better understanding of the effect of output delays and related phenomena in mechatronic systems, making it possible to design resilient control laws under the presence of uncertain time delays in measurements and obtain an acceptable performance without using a derivative action. The Furuta pendulum is a standard two-degrees-of-freedom benchmark example from the class of underactuated mechanical systems. The configuration under study includes an inherent output delay due to wireless communication used to transmit measurements of the pendulum's angular position. Our approach offers a constructive design and a procedure based on a combination of root loci and Mikhailov methods for the analysis of stability. Experiments over a laboratory platform are reported and a comparison with a standard linear state feedback control law shows the advantages of the proposed scheme.

show abstract

“…, ∞. In [16], the parameter space ( , , ) of control law [13] to -stabilize system [12] is determined.…”

Section: A Pr Controller For a Second-order Plantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Proportional Retarded Controller to Stabilize Underactuated Systems with Measurement Delays: Furuta Pendulum Case Study

Ortega-Montiel

Villafuerte-Segura

Vázquez³

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…These include proportional plus delay q 3 (s), integrator plus delay model q 4 (s), first order lag plus delay q 5 (s), first order lag plus integral plus delay q 6 (s) expressed below: If in the expression of q 3 (s) there are two different gains for the two terms, then we obtain the proportional retarded controller: q 7 (s) = K p + K r e −sτm . Furthermore, Villafuerte, Mondié & Garrido (2013) showed that proportional retarded controller outperforms a PD controller on an experimental DC-servomotor setup. Obviously, any control among PID type results in a characteristic equation that depends on the control parameters.…”

Section: Introductionmentioning

confidence: 99%

Some insights into the migration of double imaginary roots under small deviation of two parameters

Irofti

Boussaada

et al. 2018

Automatica

View full text Add to dashboard Cite

This paper studies the migration of double imaginary roots of the systems' characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right half-plane, and the other moves to the left half-plane. When the parameters move into the S-sector, both roots move either to the left half-plane or the right half-plane depending on the sign of a quantity that depends on the characteristic function and its derivatives up to the third order.

show abstract

“…The ideas behind this work were inspired by the results presented in [20] where the PMD controller is introduced, and also in [23] where further advancements are reported. In the case of the IR controller, the measurement noise attenuation capabilities of the PMD are enhanced by including an integral action which also makes possible to reject constant disturbances.…”

Section: Introductionmentioning

confidence: 99%