Defragilization in optimal design and its application to fixed structure LQ controller design

Norlander, T.; Mäkilä, P. M.

doi:10.1109/87.930969

Cited by 6 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Accordingly, even though the designed controllers are robust with respect to system uncertainties, they may be very sensitive to their own uncertainties. Recently, much attention has been paid to the so-called fragility problems of controllers [14][15]. This problem is basically associated with performance decrease of a closed-loop system due to the inaccuracies in the controller implementation [16].…”

Section: Introductionmentioning

confidence: 99%

Reliable Robust Controller for Half-Car Active Suspension Systems Based on Human-Body Dynamics

Gudarzi

2016

FU Mech Eng

View full text Add to dashboard Cite

The paper investigates a non-fragile robust control strategy for a half-car active suspension system considering human-body dynamics. A 4-DoF uncertain vibration model of the driver’s body is combined with the car’s model in order to make the controller design procedure more accurate. The desired controller is obtained by solving a linear matrix inequality formulation. Then the performance of the active suspension system with the designed controller is compared to the passive one in both frequency and time domain simulations. Finally, the effect of the controller gain variations on the closed-loop system performance is investigated numerically.

show abstract

Section: Introductionmentioning

confidence: 99%

Reliable Robust Controller for Half-Car Active Suspension Systems Based on Human-Body Dynamics

Gudarzi

2016

FU Mech Eng

View full text Add to dashboard Cite

show abstract

“…Under the suitable hypothesis similar to the one used in Collins and Zhao (2001), D'Andrea and Istepanian (2002), Norlander and Mäkilä (2001), Yang et al (2001) and Yee et al (2000) we study the design of the H ∞ output feedback controller of a fixed order with FWL considerations. A novel FWL robust control performance measure is proposed which takes into account the standard robust control requirements, such as plant uncertainties and input-output characteristics, as well as the FWL effects on controller implementation.…”

Section: Introductionmentioning

confidence: 99%

“…The works (Mahmoud, 2004(Mahmoud, , 2005Park, 2004;Yang et al, 2000;Yee et al, 2001) hypothesize that the controller parameter perturbation block is 2-norm bounded, while the works (Collins & Zhao, 2001;D'Andrea & Istepanian, 2002;Norlander & Mäkilä, 2001;Yang et al, 2001;Yee et al, 2000) use a more suitable hypothesis which claims that every parameter perturbation is independent and is magnitude bounded. The methods of D'Andrea and Istepanian (2002) and Yee et al (2000) deal with static state feedback, while the LQ control of a fixed order and PID control are studied in Norlander and Mäkilä (2001) and Collins and Zhao (2001), respectively. A common Lyapunov function matrix is sought in Yang et al (2001) for all the vertices of the FWL perturbation hypercube in designing a H 2 controller of fixed order, but the huge number of these vertices can result in excessive complexity in practical computation.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we deal with the second type of FWL errors. Specifically we consider FWL parameter representation errors in the design of robust controllers.Most of the existing researches (Collins & Zhao, 2001;D'Andrea & Istepanian, 2002;Mahmoud, 2004Mahmoud, , 2005Norlander & Mäkilä, 2001;Park, 2004;Yang, Wang, & Soh, 2000Yee, Yang & Wang, 2000;Yee, Yang, & Wang, 2001) refer to robust digital control design with the consideration of FWL parameter representation errors as non-fragile/defragile/resilient control. The works (Mahmoud, 2004(Mahmoud, , 2005Park, 2004;Yang et al, 2000; Wu et al / Automatica 45 (2009) [2850][2851][2852][2853][2854][2855][2856] 2851 Yee et al, 2001) hypothesize that the controller parameter perturbation block is 2-norm bounded, while the works (Collins & Zhao, 2001;D'Andrea & Istepanian, 2002;Norlander & Mäkilä, 2001;Yang et al, 2001;Yee et al, 2000) use a more suitable hypothesis which claims that every parameter perturbation is independent and is magnitude bounded.…”

mentioning

confidence: 99%

“…The methods of D 'Andrea and Istepanian (2002) and Yee et al (2000) deal with static state feedback, while the LQ control of a fixed order and PID control are studied in Norlander and Mäkilä (2001) and Collins and Zhao (2001), respectively. A common Lyapunov function matrix is sought in Yang et al (2001) for all the vertices of the FWL perturbation hypercube in designing a H 2 controller of fixed order, but the huge number of these vertices can result in excessive complexity in practical computation.Under the suitable hypothesis similar to the one used in Collins and Zhao (2001), D'Andrea andIstepanian (2002), Norlander and Mäkilä (2001), Yang et al (2001) and Yee et al (2000) we study the design of the H ∞ output feedback controller of a fixed order with FWL considerations. A novel FWL robust control performance measure is proposed which takes into account the standard robust control requirements, such as plant uncertainties and input-output characteristics, as well as the FWL effects on controller implementation.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Robust Finite Word Length controller design

Chen

et al. 2009

Automatica

View full text Add to dashboard Cite

Mixed µ theoryLinear matrix inequality Bilinear matrix inequality a b s t r a c t A novel Finite Word Length (FWL) controller design is proposed in the framework of a mixed µ theory.A robust FWL controller performance measure is first developed, which takes into account the standard robust control requirements as well as the FWL implementation considerations, and the corresponding controller design problem is naturally reformulated as a mixed µ problem which can be treated effectively with the results of the mixed µ theory.© 2009 Elsevier Ltd. All rights reserved. IntroductionRobust control capable of coping with uncertainty in plant dynamics has been the focal point of the control community for the past three decades. An implicit assumption in most of the existing robust design methods is that controllers are implemented exactly, i.e. there is no uncertainty occurring in realising controllers. In reality controllers are implemented with Finite Word Length (FWL) processors. In 1997, the fragility problem was raised in the work of (Keel & Bhattacharyya, 1997) which showed by examples that a controller achieving the largest robustness to plant uncertainty most likely has a vanishingly small closed-loop stability margin with respect to the controller parameters. Thus, a control system designed by maximising its robustness to plant uncertainty may be fragile, and the resulting fragile controller will need a processor with a very long bit length in implementation to minimise the FWL effects and therefore avoid degrading the designed closed-loop performance or even destabilising the designed stable closed-loop system. However, in many practical systems, such as $ The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Masayuki Fujita under the direction of Editor Ian R. Petersen. * Corresponding author. Tel.: +44 023 8059 666; fax: +44 023 8059 450.E-mail addresses: jwu@iipc.zju.edu.cn (J. Wu), ieligang@zjut.edu.cn (G. Li), sqc@ecs.soton.ac.uk (S. Chen), chuj@iipc.zju.edu.cn (J. Chu).mass-produced electronic consumer goods, fixed-point processors of short word length are preferred because of their advantages in component cost, chip area, operation simplicity and power consumption. Therefore, it is not a practical approach to simply pursue the optimal robustness to plant uncertainty without considering the FWL effects (Franklin, Powell & Workman, 1998;Gevers & Li, 1993;Istepanian & Whidborne, 2001).A suitable robust design approach is maintaining a suboptimal robustness to plant uncertainty while simultaneously making the controller tolerance to FWL implementation as large as possible. Through this design, a robust controller can be obtained which does not require a long word-length hardware for implementation. There exist two types of main FWL errors in digital controller implementation. The first one is the rounding errors that occur in arithmetic operations, and the second one is the parameter representation errors. Typically, the...

show abstract

Robust reliable control in vibration suppression of sandwich circular plates

Oveisi

Shakeri

2016

Engineering Structures

View full text Add to dashboard Cite

Defragilization in optimal design and its application to fixed structure LQ controller design

Cited by 6 publications

References 18 publications

Reliable Robust Controller for Half-Car Active Suspension Systems Based on Human-Body Dynamics

Reliable Robust Controller for Half-Car Active Suspension Systems Based on Human-Body Dynamics

Robust Finite Word Length controller design

Robust reliable control in vibration suppression of sandwich circular plates

Contact Info

Product

Resources

About