Optimal control of a double inverted pendulum by linearization technique

Khatoon, Shahida; Chaturvedi, D. K.; Hasan, Naimul; Istiyaque,

doi:10.1109/mspct.2017.8363988

Cited by 7 publications

(6 citation statements)

References 4 publications

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“…The motion of a double pendulum on a cart has been well-studied to date. , Although there are several types of resonator models available, a double pendulum is a relatively simple, yet highly nonlinear system . Moreover, the double pendulum simulated motion and droplet recorded motion share similar attributes as highlighted in Figure .…”

Section: Modelingmentioning

confidence: 96%

Describing Droplet Motion on Surface-Textured Ratchet Tracks with an Inverted Double Pendulum Model

Naji

Kirici²,

Javili

et al. 2021

Langmuir

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We describe the motion of a droplet on a textured ratchet track using a nonlinear resonator model. A textured ratchet track is composed of a semicircular pillar array that induces a net surface tension local gradient on a droplet placed on it. When a vertical vibration is applied, hysteresis is overcome, and the droplet moves toward the local lower energy barrier; however, due to the repetitive structure of texture, it keeps moving until the end of the track. The droplet motion depends on the amplitude and frequency of the vertical oscillation, and this dependence is nonlinear. Therefore, finding a fully analytic solution to represent this motion is not trivial. Consequently, the droplet motion remains poorly understood. In this study, we elaborate on the utility of a double pendulum as a basis for modeling the droplet motion on surfaces inducing asymmetric force. Similar to the droplet motion, resonators, such as a double pendulum, are simple, yet nonlinear systems. Moreover, an inverted double pendulum motion has key characteristics such as the two-phase motion and the double peak motion, which are also observed in the droplet motion. We use various data-processing methods to highlight the similarity between these two systems both qualitatively and quantitatively. After establishing this comparison, we propose a model that utilizes an inverted double pendulum mounted on a moving cart to successfully simulate the motion of a droplet on a ratchet track. This methodology will lead to the development of an accurate droplet-motion modeling approach, and we believe that it will be useful to understand droplet dynamics more deeply.

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Section: Modelingmentioning

confidence: 96%

Describing Droplet Motion on Surface-Textured Ratchet Tracks with an Inverted Double Pendulum Model

Naji

Kirici²,

Javili

et al. 2021

Langmuir

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“…The control performance or the performance index is measured using a quadratic cost function, which consists of the state and control input of the system. After the performance index is expressed, the optimal state feedback control gain is obtained by solving the state-dependent The LQR control strategy has been successfully implemented in a complex system such as tracking control of 2 DoF laboratory helicopter [1], double inverted pendulum [4,21], and also for tracking control of quadrotor [22]. The main reason the LQR is successfully implemented is the inherent robustness and stability properties, such as a gain margin of at least ( ) and a phase margin of ( ) degree.…”

Section: Linear Quadratic Regulatormentioning

confidence: 99%

“…The composition of the element in this weighting matrix has a significant influence to obtain the optimal performance of LQR [23]. Several works [1,4,21,22] have been selected for the diagonal form of weighting matrices, which make the performance index only as a weighted integral square error of the state and the control input. Conventionally, the weighted matrices of LQR tuned manually [4,21]; thus, it does not have the optimal performance.…”

Section: Linear Quadratic Regulatormentioning

confidence: 99%

“…Several works [1,4,21,22] have been selected for the diagonal form of weighting matrices, which make the performance index only as a weighted integral square error of the state and the control input. Conventionally, the weighted matrices of LQR tuned manually [4,21]; thus, it does not have the optimal performance. Therefore, to overcome the weighting matrices selection of LQR, the proposed PSO algorithm was developed to optimally tuned the weighting matrices and .…”

Section: Linear Quadratic Regulatormentioning

confidence: 99%

“…However, this approach is not only tedious but time-consuming. Hence, in another method, the LQR design is formulated into an optimization problem and solved ether using the evolutionary or swarm intelligence optimization algorithm such as a particle swarm optimization (PSO) [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Signature PSO: A novel inertia weight adjustment using fuzzy signature for LQR tuning

et al. 2021

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Particle swarm optimization (PSO) is an optimization algorithm that is simple and reliable to complete optimization. The balance between exploration and exploitation of PSO searching characteristics is maintained by inertia weight. Since this parameter has been introduced, there have been several different strategies to determine the inertia weight during a train of the run. This paper describes the method of adjusting the inertia weights using fuzzy signatures called signature PSO. Some parameters were used as a fuzzy signature variable to represent the particle situation in a run. The implementation to solve the tuning problem of linear quadratic regulator (LQR) control parameters is also presented in this paper. Another weight adjustment strategy is also used as a comparison in performance evaluation using an integral time absolute error (ITAE). Experimental results show that signature PSO was able to give a good approximation to the optimum control parameters of LQR in this case.

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