Control of Surge in Centrifugal Compressors by Active Magnetic Bearings

Yoon, Se Young; Lin, Zongli; Allaire, Paul E.

doi:10.1007/978-1-4471-4240-9

Cited by 65 publications

(66 citation statements)

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“…The first type of measurement is the rotor vibration magnitude for speeds ranging from 500 rpm to 16,500 rpm, in 500 rpm increments. Three separate cases are tested including the conventional integer order PID (IOPID) and FOPID controllers tuned by the DE algorithm and the LQG controller that was previously designed in [49].…”

Section: Experimental Test Of Lateral Rotor Suspensionmentioning

confidence: 99%

“…The controller structure will have the same form as in the lateral dynamics design, where the FOPID controller is coupled with a second order low pass filter. The objective functions will be similar to the objectives defined for the H ∞ controller design for axial rotor support in [49]. The objective functions will combine the weighting functions with the sensitivity function S, the complementary sensitivity function T, the plant transfer function G, and the controller transfer function K, in order to specify the desired performance in the frequency domain.…”

Section: Design Of Fopid Controllermentioning

confidence: 99%

“…For comparison, the conventional PID controller is tuned based on the same objectives and algorithms as for the FOPID controller. Moreover, performances based on the LQG controller that were designed for the same system reported in [49] are compared with both the FOPID and PID controllers in Table 6. As shown in Table 6 and Figure 22, the stability margin of all controllers fall within Zone A specification (smaller than 3).…”

mentioning

confidence: 99%

“…In the above objective functions, the weighting functions are defined in [49], based on the interconnected system shown in Figure 27, as follows,…”

mentioning

confidence: 99%

“…Moreover, performance based on the H ∞ controller that was designed for the same system reported in [49] are compared with both the FOPID and the IOPID controllers in Table 9.…”

mentioning

confidence: 99%

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Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Anantachaisilp¹,

Lin

2017

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Abstract:One of the key issues in control design for Active Magnetic Bearing (AMB) systems is the tradeoff between the simplicity of the controller structure and the performance of the closed-loop system. To achieve this tradeoff, this paper proposes the design of a fractional order Proportional-Integral-Derivative (FOPID) controller. The FOPID controller consists of only two additional parameters in comparison with a conventional PID controller. The feasibility of FOPID for AMB systems is investigated for rotor suspension in both the radial and axial directions. Tuning methods are developed based on the evolutionary algorithms for searching the optimal values of the controller parameters. The resulting FOPID controllers are then tested and compared with a conventional PID controller, as well as with some advanced controllers such as Linear Quadratic Gausian (LQG) and H ∞ controllers. The comparison is made in terms of various stability and robustness specifications, as well as the dimensions of the controllers as implemented. Lastly, to validate the proposed method, experimental testing is carried out on a single-stage centrifugal compressor test rig equipped with magnetic bearings. The results show that, with a proper selection of gains and fractional orders, the performance of the resulting FOPID is similar to those of the advanced controllers.

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Section: Experimental Test Of Lateral Rotor Suspensionmentioning

confidence: 99%

Section: Design Of Fopid Controllermentioning

confidence: 99%

mentioning

confidence: 99%

“…In the above objective functions, the weighting functions are defined in [49], based on the interconnected system shown in Figure 27, as follows,…”

mentioning

confidence: 99%

“…Moreover, performance based on the H ∞ controller that was designed for the same system reported in [49] are compared with both the FOPID and the IOPID controllers in Table 9.…”

mentioning

confidence: 99%

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Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Anantachaisilp¹,

Lin

2017

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On polynomial hyperreduction for nonlinear structural mechanics

Martynov

Wever

2019

Numerical Meth Engineering

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Summary This paper proposes an approach for hyperreduction of nonlinear structural mechanics equations. For hyperreduction, the nonlinear term is approximated by the third‐degree multivariate polynomials represented in terms of a monomial basis. The chosen basis leads to an ill‐conditioned minimization problem with the multivariate Vandermonde matrix. The condition number of the resulting problem is significantly improved by choosing an appropriate sparse subset of the initial basis. As a byproduct of the sparse basis, the evaluation time for the hyperreduced model is reduced drastically. The performance of the new approach is demonstrated for two typical applications.

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Design of PID control for planar uncertain nonlinear systems with input delay

Lyu

Lin

2021

Intl J Robust & Nonlinear

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This article presents a PID control design for a class of planar uncertain nonlinear systems with bounded time‐varying input delay. The delay is unknown with a known bound. The class of systems is characterized by the bounds on the growth rates of the nonlinear function in the system model. Based on these bounds on the growth rates, the system is placed in a linear differential inclusion, a convex hull with four linear systems as vertices. For a given set of PID control coefficients, a Lyapunov–Krasovskii functional is constructed that leads to sufficient conditions, in the form of linear matrix inequalities in the bound on the time delay, a positive scalar and two positive definite matrices, under which the equilibrium solution corresponding to the desired set point of the outputs of all vertex linear systems and, hence, that of the original uncertain nonlinear system, is globally uniformly asymptotically stable. With the bound on the time delay as a variable, an optimization problem with linear matrix inequalities as constraints can be formulated to determine the largest admissible bound on the time delay for the closed‐loop system under the given PID controller. By viewing the PID control coefficients as additional free variables, the optimization problem is then adapted for the design of the PID coefficients for the largest admissible bound on the time delay. The design is then applied to a magnetic suspension system. Simulation results illustrate the design algorithm and the performance of the resulting PID controller.

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Control of Surge in Centrifugal Compressors by Active Magnetic Bearings

Cited by 65 publications

References 0 publications

Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

On polynomial hyperreduction for nonlinear structural mechanics

Design of PID control for planar uncertain nonlinear systems with input delay

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