Model reduction based on triangle realization with pole retention

Nguyen, Cong Huu; Vu, Kien Ngoc; Trung, Hai

doi:10.12988/ams.2015.5290

Cited by 3 publications

(8 citation statements)

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“…To control the self-balancing two-wheel vehicle according to the inverted pendulum principle, there are various methods such as PD [20], PID [17][18][19], LQG and MPC [21], SMC [25][26][27], and robust control [11,[28][29][30][31][32][33][34][35][36][37][38]. However, when a two-wheel vehicle works in reality, it will suffer many uncertain effects such as load, noise, and external force.…”

Section: Introductionmentioning

confidence: 99%

“…erefore, the two-wheel vehicle model can be considered as an uncertain object [10]. To control unstable objects, there are many different algorithms, of which the most used algorithm is sliding-mode control (SMC) [25][26][27] and robust control algorithm [11,[28][29][30][31][32][33][34][35][36][37][38]. Key features of the SMC are its ability to resist parameter uncertainty, a fast response rate, no sensitivity to bounded external disturbances, and simple design computation.…”

Section: Introductionmentioning

confidence: 99%

“…e robust optimal control algorithm RH¥ [11,[28][29][30][31][32][33][34][35][36][37][38] is designed to shape the system's response to achieve the desired behavior and maintain this behavior from model parameter variation or disturbances. However, to ensure the two above functions, the robust optimal controller H¥ is often high.…”

Section: Introductionmentioning

confidence: 99%

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Design Low-Order Robust Controller for Self-Balancing Two-Wheel Vehicle

Quang

2021

Mathematical Problems in Engineering

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When there is no driver, balancing the two-wheel vehicle is a challenging but fascinating problem. There are various solutions for maintaining the balance of a two-wheel vehicle. This article presents a solution for balancing a two-wheel vehicle using a flywheel according to the inverted pendulum principle. Since uncertainties influence the actual operating environment of the vehicle, we have designed a robust controller RH∞ to maintain the vehicle equilibrium. Robust controllers often have a high order that can affect the actual control performance; therefore, order reduction algorithms are proposed. Using Matlab/Simulink, we compared the performance of the control system with different reduced-order controllers to choose a suitable low-order controller. Finally, experimental results using a low-order robust controller show that the vehicle balances steadily in different scenarios: no-load, variable load, stationary, and moving.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design Low-Order Robust Controller for Self-Balancing Two-Wheel Vehicle

Quang

2021

Mathematical Problems in Engineering

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“…The BT algorithm and other algorithms [14][15][16] are mainly applied to stable linear systems because the original concepts of the BT method (controllability Gramian and observability Gramian) are always accompanied by the requirement that the system is stable, ie the system has all the poles on the left of the imaginary axis. In practical applications, however, higher-order linear models (higher-order object models, higher-order controllers [17][18][19]) may be unstable. Therefore, to meet the requirements of the problem of order reduction, algorithms need to be capable to reduce the order of both stable and unstable systems.…”

Section: Introductionmentioning

confidence: 99%

“…To solve the problem of order reduction for unstable systems, there are two strategies:  Strategy 1 (indirect order reduction algorithm): Firstly, the unstable original system is separated into stable and unstable parts. After that, an order reduction algorithm is applied to the stable part [17,18], [20][21][22][23]. Finally, we add the stable reduced-order part with the unstable part.…”

Section: Introductionmentioning

confidence: 99%

Model reduction of unstable systems based on balanced truncation algorithm

Quang

2021

IJECE

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Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms.

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Design Low Order Robust Controller for the Generator’s Rotor Angle Stabilization PSS System

2021

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The electrical system's problem stabilizes the electrical system with three primary parameters: rotor angle stability, frequency stability, and voltage stability. This paper focuses on the problem of designing a low-order stable optimal controller for the generator rotor angle (load angle) stabilization system with minor disturbances. These minor disturbances are caused by lack of damping torque, change in load, or change in a generator during operation. Using the RH∞optimal robust design method for the Power System Stabilizer (PSS) to stabilize the generator’s load angle will help the PSS system work sustainably under disturbance. However, this technique's disadvantage is that the controller often has a high order, causing many difficulties in practical application. To overcome this disadvantage, we propose to reduce the order of the higher-order optimal robust controller. There are two solutions to reduce order for high-order optimal robust controller: optimal order reduction according to the given controller structure and order reduction according to model order reduction algorithms. This study selects the order reduction of the controller according to the model order reduction algorithms. In order to choose the most suitable low-order optimal robust controller that can replace the high-order optimal robust controller, we have compared and evaluated the order-reducing controllers according to many model order reduction algorithms. Using robust low-order controllers to control the generator’s rotor angle completely meets the stabilization requirements. The research results of the paper show the correctness of the controller order reduction solution according to the model order reduction algorithms and open the possibility of application in practice. Doi: 10.28991/esj-2021-01299 Full Text: PDF

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Model reduction based on triangle realization with pole retention

Cited by 3 publications

References 1 publication

Design Low-Order Robust Controller for Self-Balancing Two-Wheel Vehicle

Design Low-Order Robust Controller for Self-Balancing Two-Wheel Vehicle

Model reduction of unstable systems based on balanced truncation algorithm

Design Low Order Robust Controller for the Generator’s Rotor Angle Stabilization PSS System

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