Convex Synthesis of SNI Controllers Based on Frequency-Domain Data: MEMS Nanopositioner Example

Nikooienejad, Nastaran; Moheimani, S. O. Reza

doi:10.1109/tcst.2021.3080577

Cited by 13 publications

(3 citation statements)

References 35 publications

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“…Let us now define a sliding surface sφ = ėφ + λ φ e φ for the roll dynamics (7) following [26], where λ φ is positive and the roll angle error is e φ = φ − φ d . If a reaching law ṡ = −k φ sgn(s φ ), k φ > 0 is selected and a Lyapunov candidate…”

Section: Linearisation Using Smcmentioning

confidence: 99%

“…This paper aims to design a simple yet effective cooperative controller for a group of networked tricopter drones utilising the NI theory, characteristic loci technique and SMC-based linearisation principles. Negative Imaginary (NI) systems theory has attracted the interest of control theorists and practising engineers due to its potential to solve various real-life engineering challenges, like vibration control of lightly-damped systems [4], cantilever beams [5], [6]; nano-positioning applications [7]; cooperative train platooning [8]; control of dissipative systems [9]- [11]; etc. Due to a simple robust stability criterion depending only on the loop gain at zero frequency (known as the DC loop gain condition [4]), NI theory has gained a lot of traction.…”

Section: Introductionmentioning

confidence: 99%

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Cooperative Control of Multi-Tilt Tricopter Drones Applying a ‘Mixed’ Negative Imaginary and Strict Passivity Technique

Abara,

Bhowmick,

Lanzon

2023

2023 European Control Conference (ECC)

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This paper develops a cooperative controller for a fleet of multi-tilt tricopter drones modelled as Negative Imaginary (NI) systems via closed-loop linearisation exploiting Sliding-Mode Control (SMC) technique. The multi-tilt tricopter model is derived from the first principles, and the SMC method is invoked to obtain a closed-loop linear model of the tricopter plant with six outputs and six inputs. A subspacebased system identification algorithm is developed to identify the linearised drone model enforcing the NI property. The primary control objective is to design a distributed 'mixed' NI and strictly Passive control protocol so that the tricopter agents asymptotically reach the desired formation and keep tracking the target. Instead of the Lyapunov approach, the characteristic loci method is used to prove the asymptotic convergence of the trajectory tracking error. Finally, an exhaustive simulation case study is carried out on a fleet of six multi-tilt tricopter drones to demonstrate the feasibility of the cooperative controller presented in this work.

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Section: Linearisation Using Smcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cooperative Control of Multi-Tilt Tricopter Drones Applying a ‘Mixed’ Negative Imaginary and Strict Passivity Technique

Abara,

Bhowmick,

Lanzon

2023

2023 European Control Conference (ECC)

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“…In comparison to passivity theory, which can deal with systems of relative degree zero and one [19], an advantage of NI systems theory is that it can deal with systems of relative degree zero, one and two [20], [21]. Since it was introduced, NI systems theory has attracted attention among control theorists (see e.g., [22]- [28]) and has found its application in many fields including nanopositioning control [29]- [33], the control of lightly damped structures [9], [34], [35], and the control of electrical power systems [36], [37], etc.…”

Section: Introductionmentioning

confidence: 99%

A negative imaginary approach to hybrid integrator-gain system control

Shi

Nikooienejad

Petersen

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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We propose a discrete-time integral resonant control (IRC) approach for negative imaginary (NI) systems, which overcomes several limitations of continuous-time IRC. We show that a discrete-time IRC has a step-advanced negative imaginary property. A zero-order hold-sampled NI system can be asymptotically stabilized using a discrete-time IRC with suitable parameters. A hardware experiment is conducted where a highspeed flexure-guided nanopositioner is efficiently damped using the proposed discrete-time IRC with the discrete-time controller being implemented in FPGA hardware at the sampling rate of 1.25 MHz.

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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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Convex Synthesis of SNI Controllers Based on Frequency-Domain Data: MEMS Nanopositioner Example

Cited by 13 publications

References 35 publications

Cooperative Control of Multi-Tilt Tricopter Drones Applying a ‘Mixed’ Negative Imaginary and Strict Passivity Technique

Cooperative Control of Multi-Tilt Tricopter Drones Applying a ‘Mixed’ Negative Imaginary and Strict Passivity Technique

A negative imaginary approach to hybrid integrator-gain system control

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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