Stability Analysis of Interconnected Systems With “Mixed” Negative-Imaginary and Small-Gain Properties

Patra, S.; Lanzon, Alexander

doi:10.1109/tac.2011.2122670

Cited by 95 publications

(68 citation statements)

References 20 publications

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“…This shows that R(0) is also non-singular and thus,R(0) > 0. This concludes the proof of the lemma We now present a theorem [1,7,13,[15][16][17]19] which provides the main robustness and stability analysis result involving the positive-feedback interconnection of an NI system and an SNI system as shown in Fig. 1.…”

Section: Lemma 2 If R(s) Is Negative Imaginary and R S (S) Is Strictlymentioning

confidence: 91%

“…The concept of negative imaginary system was first introduced in [1,2] and subsequently, several research works have been explored to develop analysis and synthesis frameworks for negative imaginary (NI) systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Negative imaginary systems are important in engineering practice as this class of system appears quite often in practical problems, for example, when considering the transfer function from force actuators to collocated position sensor in lightly damped structure [1][2][3][4]6,9,[14][15][16][17]19,22], from input voltage to output voltage in electrical active filter circuits [13], from input voltage to shaft rotational velocity in a DC motor [7].…”

Section: Introductionmentioning

confidence: 99%

“…Negative imaginary systems are important in engineering practice as this class of system appears quite often in practical problems, for example, when considering the transfer function from force actuators to collocated position sensor in lightly damped structure [1][2][3][4]6,9,[14][15][16][17]19,22], from input voltage to output voltage in electrical active filter circuits [13], from input voltage to shaft rotational velocity in a DC motor [7]. Negative-imaginary property also occurs in nano-positioning systems [11,23].…”

Section: Introductionmentioning

confidence: 99%

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LMI based robust state feedback control of negative-imaginary systems

Choudhary

2015

Int. J. Dynam. Control

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The importance of robust feedback control for uncertain negative imaginary system lies in its practical relevance and engineering applications, for example, lightly damped flexible structures with collocated position sensors and force actuators. This article investigates an LMI based robust static state internally stabilizing feedback controller of the negative imaginary system in presence of strictly negative imaginary uncertainties. The paper first presents some basic theory of negative imaginary systems and then, a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems. The paper provides a systematic controller synthesis procedure based on negative imaginary lemma to achieve robustness in the feedback control of negative imaginary systems. To show the effectiveness of controller synthesis method, one design example is considered and a static state-feedback controller is constructed to force the plant to be stable. The simulation results of this article demonstrate the usefulness of the design method and we believe that feedback control of the negative imaginary system can benefit control engineering practitioners in a number of ways.

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Section: Lemma 2 If R(s) Is Negative Imaginary and R S (S) Is Strictlymentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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LMI based robust state feedback control of negative-imaginary systems

Choudhary

2015

Int. J. Dynam. Control

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“…However, it is often seen that many practical systems do not always belong to the specific class, i.e., only passivity or only negative-imaginary over the whole frequency range (Griggs et al 2007(Griggs et al , 2009Patra and Lanzon 2011;). There are many other systems which may have mixed passivity and small-gain (Griggs et al 2007(Griggs et al , 2009 properties or mixed negative-imaginary and small-gain (Patra and Lanzon 2011) properties.…”

Section: Introductionmentioning

confidence: 99%

“…There are many other systems which may have mixed passivity and small-gain (Griggs et al 2007(Griggs et al , 2009 properties or mixed negative-imaginary and small-gain (Patra and Lanzon 2011) properties. An unconditional stability analysis for negative feedback interconnected systems with mixed passivity and small-gain properties is presented in Griggs et al (2007), whereas shows conditional stability between systems with mixed negative-imaginary and small-gain properties using positive feedback.…”

Section: Introductionmentioning

confidence: 99%

Design and Implementation of Feedback Resonance Compensator in Hard Disk Drive Servo System: A Mixed Passivity, Negative-Imaginary and Small-Gain Approach in Discrete Time

Rahman

Mamun

Yao

et al. 2015

J Control Autom Electr Syst

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This paper presents a feedback resonance compensator designed in a simple and yet efficient way to suppress the effects of resonant modes of voice coil motor actuator used in hard disk drive (HDD) servo system. A velocity feedback controller is chosen as the feedback resonance compensator. Resonant modes of the actuator prohibit bandwidth to be pushed to higher frequencies and it causes large oscillations to the closed-loop system response. Therefore, effective compensation of mechanical resonant modes is one of the design challenges in HDD servomechanism. The proposed design is based on a mixed passivity, negative-imaginary and small-gain approach in discrete time which results in a robust stable controller. Firstly, stability of discrete-time interconnected system is analyzed using mixed passivity, negative-imaginary and small-gain properties. These results are analogous to previously established continuous-time case. Nowadays most of the control design is done in discrete time. Hence, this paper provides a base for discretization of mixed system with passivity, negativeimaginary and small-gain properties. Secondly, a velocity feedback controller for resonance compensation is designed using this mixed approach. Simulation and experimental results substantiate the effectiveness of the controller.

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Properties of interconnected negative imaginary systems and extension to formation‐containment control of networked multi‐UAV systems with experimental validation results

Su,

Bhowmick,

Lanzon

2023

Asian Journal of Control

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This paper extends the properties of a positive feedback interconnection of two negative imaginary (NI) systems to multi‐agent NI systems and proposes a new formation‐containment control methodology relying on the characteristic loci technique. Inspired by recent applications of NI and passivity‐based control techniques in the multi‐agent systems (MAS) domain, a new formation‐tracking and containment control scheme is developed for a class of networked multi‐UAV systems. The proposed scheme offers a two‐stage and two‐loop control configuration where the inner loop uses a cascaded PID controller to ensure stable hovering of the UAVs, and the outer loop deploys a distributed “mixed” SNI and strictly passive controller to achieve the formation‐containment objectives. This scheme works with a dynamic output feedback control strategy; hence, it offers advantages when the full‐state measurement is not possible. In contrast to the well‐known Lyapunov theory‐based cooperative control schemes, the present one exploits the characteristic loci technique to prove the formation‐tracking and containment phenomena theoretically. The paper also provides experimental validation results on a fleet of Crazyflie 2.1 nano quadcopters.

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Stability Analysis of Interconnected Systems With “Mixed” Negative-Imaginary and Small-Gain Properties

Cited by 95 publications

References 20 publications

LMI based robust state feedback control of negative-imaginary systems

LMI based robust state feedback control of negative-imaginary systems

Design and Implementation of Feedback Resonance Compensator in Hard Disk Drive Servo System: A Mixed Passivity, Negative-Imaginary and Small-Gain Approach in Discrete Time

Properties of interconnected negative imaginary systems and extension to formation‐containment control of networked multi‐UAV systems with experimental validation results

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