Design of Proportional-Minus-Delay Action Feedback Controllers for Second- and Third-Order Systems

Swisher, G. M.; Tenqchen, Shing

doi:10.23919/acc.1988.4789724

Cited by 13 publications

(18 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…On the other hand, some authors (Tallman and Smith 1958, Rudin 1976, Suh and Bien 1979, 1980, Marshall and Salehi 1982, Swisher and Tenqchen 1988, ha ve used intentional time delays in the controller design of ordinary systems. These studies have shown that the performance of the controlled system may be improved by the judicious use of time-delay actions.…”

Section: Introductionmentioning

confidence: 98%

“…The proportional minus delay (PMD) controller for second-order systems has been studied in Suh andBien (1979, 1980), where it has been shown that an appropriate PMD controller performs an averaged derivative action and can thus replace the conventional proportional plus derivative (PD) controller, showing quick responses to input changes but being insensitive to highfrequency noises. The use of PMD controllers has been extended to third-order systems (Swisher and Tenqchen 1988). However, controllers using time-delay actions have been confined to single-input/single-output (SISO) second-or third-order systems and have no theoretical results on the analysis of their controllers.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Performance improvement using time delays in multivariable controller design

Кwon

Lee

Kim

1990

International Journal of Control

View full text Add to dashboard Cite

A new controller for linear multivariable ordinary systems is suggested in which distributed delays are included in the feedback loop. A general design approach to obtain this type of controller is suggested. It is shown that the resulting closed-loop system is asymptotically stable under some sufficient conditions. Sufficient conditions are derived under which the disturbance attenuation, the robustness against parameter variations, and the time-delay stability margins are improved by the proposed controller. The state feedback tracking controller and the dual-state observer are obtained by modification of the proposed controller.

show abstract

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Performance improvement using time delays in multivariable controller design

Кwon

Lee

Kim

1990

International Journal of Control

View full text Add to dashboard Cite

show abstract

“…e deliberate use of retarded actions to stabilize a system is a topic that has been investigated in recent decades, among which are the pioneering contributions of [17][18][19][20][21][22][23][24][25][26][27][28]. Concerning derivative-free control based schemes, such as the proportional retarded (PR) scheme [19,25,[29][30][31], which consists in using the relation between the time derivative approximations in terms of a differential difference equation, involving a time delay.…”

Section: Introductionmentioning

confidence: 99%

Cascade Delayed Controller Design for a Class of Underactuated Systems

et al. 2020

View full text Add to dashboard Cite

In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot.

show abstract

“…Furthermore, a Furuta pendulum case study, where the underactuated variable is subject to an inherent output delay due to wireless signal transmission, is presented. 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].…”

Section: Introductionmentioning

confidence: 99%

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

Design of Proportional-Minus-Delay Action Feedback Controllers for Second- and Third-Order Systems

Cited by 13 publications

References 5 publications

Performance improvement using time delays in multivariable controller design

Performance improvement using time delays in multivariable controller design

Cascade Delayed Controller Design for a Class of Underactuated Systems

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

Contact Info

Product

Resources

About