Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum
The inverted pendulum is a non-linear control problem permanently tending towards instability. The main aim of this study is to design a controller capable enough to work within the given conditions while also keeping the pendulum erect given the impulsive movement of the cart to which it is joint v...
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| Format: | Article |
| Language: | English |
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National Institute for Aerospace Research “Elie Carafoli” - INCAS
2021-09-01
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| Series: | INCAS Bulletin |
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| Online Access: | https://bulletin.incas.ro/files/mirza__vol_13_iss_3.pdf |
| _version_ | 1818670287367962624 |
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| author | K. Z. MIRZA |
| author_facet | K. Z. MIRZA |
| author_sort | K. Z. MIRZA |
| collection | DOAJ |
| description | The inverted pendulum is a non-linear control problem permanently tending towards instability. The main aim of this study is to design a controller capable enough to work within the given conditions while also keeping the pendulum erect given the impulsive movement of the cart to which it is joint via a hinge. The first half of the paper presents the mathematical modelling of the dynamic system, together with the design of a linear quadratic regulator (LQR). This paper also discusses a novel adaptive control mechanism employing a Kalman filter for the mobile inverted pendulum system (MIPS). In the second half of the paper, a Gaussian Quadratic Linear Controller (LQG) is adapted to improve on previous deficiencies. The simulation is done through Simulink and results show that both controllers are capable of managing the multiple output model. However, data from simulations clearly showed that an LQG controller is a better choice. |
| first_indexed | 2024-12-17T07:05:43Z |
| format | Article |
| id | doaj.art-aacdab2fc8344562872cb362ad560777 |
| institution | Directory Open Access Journal |
| issn | 2066-8201 2247-4528 |
| language | English |
| last_indexed | 2024-12-17T07:05:43Z |
| publishDate | 2021-09-01 |
| publisher | National Institute for Aerospace Research “Elie Carafoli” - INCAS |
| record_format | Article |
| series | INCAS Bulletin |
| spelling | doaj.art-aacdab2fc8344562872cb362ad5607772022-12-21T21:59:09ZengNational Institute for Aerospace Research “Elie Carafoli” - INCASINCAS Bulletin2066-82012247-45282021-09-01133799010.13111/2066-8201.2021.13.3.7Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted PendulumK. Z. MIRZA0Department of Mechatronics, MPSTME, NMIMS, Mumbai - 400058, India, Khojasteh.mirza40@nmims.edu.inThe inverted pendulum is a non-linear control problem permanently tending towards instability. The main aim of this study is to design a controller capable enough to work within the given conditions while also keeping the pendulum erect given the impulsive movement of the cart to which it is joint via a hinge. The first half of the paper presents the mathematical modelling of the dynamic system, together with the design of a linear quadratic regulator (LQR). This paper also discusses a novel adaptive control mechanism employing a Kalman filter for the mobile inverted pendulum system (MIPS). In the second half of the paper, a Gaussian Quadratic Linear Controller (LQG) is adapted to improve on previous deficiencies. The simulation is done through Simulink and results show that both controllers are capable of managing the multiple output model. However, data from simulations clearly showed that an LQG controller is a better choice.https://bulletin.incas.ro/files/mirza__vol_13_iss_3.pdflinear quadratic regulatorkalman filterlinear quadratic gaussian controllerinverted pendulum |
| spellingShingle | K. Z. MIRZA Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum INCAS Bulletin linear quadratic regulator kalman filter linear quadratic gaussian controller inverted pendulum |
| title | Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum |
| title_full | Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum |
| title_fullStr | Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum |
| title_full_unstemmed | Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum |
| title_short | Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum |
| title_sort | linear quadratic gaussian regulator for the nonlinear observer based control of a dynamic base inverted pendulum |
| topic | linear quadratic regulator kalman filter linear quadratic gaussian controller inverted pendulum |
| url | https://bulletin.incas.ro/files/mirza__vol_13_iss_3.pdf |
| work_keys_str_mv | AT kzmirza linearquadraticgaussianregulatorforthenonlinearobserverbasedcontrolofadynamicbaseinvertedpendulum |