Nonlinear Estimation Methods: Polynomial Systems Approach

Grimble, M.J.; Majecki, Paweł

doi:10.1007/978-1-4471-7457-8_12

Cited by 2 publications

(3 citation statements)

References 36 publications

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“…The optimal control problem involves the minimization of the cost function: J=Eϕ 0 T t*ϕ 0 (t) |t (12) where: ϕ 0 t=P c (z -1 )et+(F c u)(t) (13) with error signal e(t), error weighting P c z -1 =P cd -1 z -1 P cn (z -1 ), control signal u(t) and control weighting (F c u)(t)=z -Λ 0 (F ck u)(t).…”

Section: ) Cascade Compensator Amd Loop Gainmentioning

confidence: 99%

Multiple Degrees of Freedom Active Motion Control of a Hydraulically Actuated Crane

Balan

Majecki

Grimble

et al. 2021

OCEANS 2021: San Diego – Porto

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As offshore wind farms become larger and further from the shore, there are strong economic and climate incentives to perform transfers required for operations and maintenance from floating vessels, rather than employing expensive and slow jack up rigs. However, successful transfers of heavy and sensitive equipment from a floating vessel (in all but benign sea/wind conditions) are heavily dependent on multiple degrees of freedom (DoF), high performance control. Two control design methods were employed to assess the viability of heavy lifts from floating vessels through a simulation approach using Simulink. The crane system was first modelled to operate under simulated vessel motions given by sea states with a significant wave height of 5 m and maximum wave frequency of 1 rad/s. Then, traditional control (feedback and feedforward) was designed to achieve motion compensation with steady-state position errors under 20 cm. To achieve an improved performance, a more robust controller architecture was required, thus the nonlinear generalized minimum variance (NGMV) control algorithm was chosen for this application.Due to its ability to compensate for significant system nonlinearities and the ease of implementation NGMV was a good candidate for the task at hand. Tuning the controller parameters to stabilize the system can also be based on previous classical, say PID, control solutions. Simulations showed NGMV provided an improved control performance compared to traditional control when considering model mismatch.

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Section: ) Cascade Compensator Amd Loop Gainmentioning

confidence: 99%

Multiple Degrees of Freedom Active Motion Control of a Hydraulically Actuated Crane

Balan

Majecki

Grimble

et al. 2021

OCEANS 2021: San Diego – Porto

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“…On the other hand, a controller has 2-DoF, when the reference signal and the plant output can be processed independently to obtain the control signal. The advantages of using a 2-DoF control system are well known: the closed-loop properties can be configured independently of the reference tracking transfer function (Grimble, 1994). This possibility results from the separation between the response to the reference signal and the feedback transfer function.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, some interesting works can be mentioned. The initial contributions of Limebeer et al (1993) and Grimble (1994), where the problem is formulated into a general framework. The approach of Hoover et al (2004) which propose a simple single-input-single-output 2-DoF pole-placement design method that provides ℓ 2 -optimal tracking of a given reference signal and Vilanova (2008), where the problem of optimal design of the reference controller have been addressed by the optimization of a linear quadratic Gaussian type cost function.…”

Section: Introductionmentioning

confidence: 99%

Optimal tracking in two-degree-of-freedom control systems: Coupled tank system

Teppa,

FAGGIONI,

GARCIA

2023

JART

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This article presents an optimal design of a two-degree-of-freedom (2-DoF) controller that will lead to zero asymptotic steady-state tracking error. The reference inputs are chosen from the set of steps, ramps, and other persistent signals used currently. The main idea is to transform the tracking 2-DoF problem into an equivalent state-space feedback-control synthesis one. Where, an internal model of the reference input is introduced. Then, through the linear quadratic regulator (LQR) technique, the desired performance objectives are addressed by minimizing a quadratic cost function. Finally, the computed state-feedback optimal gains are linked to the polynomials used within the 2-DoF formalism. The fundamental aspect of the design is that it only utilizes the measurable information of the plant provided by its inputs and outputs and take advantage of efficient state-space numerical algorithms. The proposed method is applied to a coupled-tank system, the results achieved confirm the effectiveness of the approach.

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Nonlinear Estimation Methods: Polynomial Systems Approach

Cited by 2 publications

References 36 publications

Multiple Degrees of Freedom Active Motion Control of a Hydraulically Actuated Crane

Multiple Degrees of Freedom Active Motion Control of a Hydraulically Actuated Crane

Optimal tracking in two-degree-of-freedom control systems: Coupled tank system

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