Stabilization of a Cart-Inverted Pendulum with Interconnection and Damping Assignment Passivity-Based Control Focusing on the Kinetic Energy Shaping

Yokoyama, Kazuo; Takahashi, Masaki

doi:10.1299/jsdd.4.698

Cited by 7 publications

(7 citation statements)

References 19 publications

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“…Figures 7 (a) Although the large domain of attraction is achieved, the speed of the convergence is very slow. Therefore, we utilized knowledge of the trade-off between performance and the domain, which was reported in our previous study (17) , when we designed the parameters of the IDA-PBC controller in Table 2.…”

Section: Simulationmentioning

confidence: 99%

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Stabilization of a Mobile Inverted Pendulum with IDA-PBC and Experimental Verification

Yokoyama

Takahashi

2011

JSDD

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Mobile inverted pendulums are needed to be stabilized at all times using a safe control method. Previous approaches were based on a linearized model or feedback linearization. In this study, interconnection and damping assignment passivity-based control (IDA-PBC) is applied. The IDA-PBC is a nonlinear control method which has been shown to be powerful to stabilize underactuated mechanical systems. Although partial differential equations (PDEs) must be solved to derive the IDA-PBC controller and it is a difficult task in general, we show that the controller for the mobile inverted pendulum can be constructed. A systematic graphical method to select controller parameters that guarantee asymptotic stability and a procedure to estimate the domain of attraction are also proposed. Using this method, the pendulum is stabilized by restricting it to a predefined angle range. Simulation results show that the IDA-PBC controller performs fast responses theoretically ensuring sufficient domain of attraction. The effectiveness of the IDA-PBC controller is also verified in experiments. Especially control performance under an impulsive disturbance on the mobile inverted pendulum is verified. The IDA-PBC achieves as fast transient performance as a linear-quadratic regulator (LQR). In addition, we show that when the pendulum inclines quickly and largely due to the disturbance, the IDA-PBC controller can stabilize it whereas the LQR cannot.

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Section: Simulationmentioning

confidence: 99%

“…In previous studies, controllers have been designed with the goal of achieving as large a domain of attraction as possible. In contrast, the authors have proposed a method to achieve fast transient performance with a trade-off in the size of the domain of attraction for a cart-inverted pendulum (17) .…”

Section: Introductionmentioning

confidence: 99%

Stabilization of a Mobile Inverted Pendulum with IDA-PBC and Experimental Verification

Yokoyama

Takahashi

2011

JSDD

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“…We utilized knowledge of the trade-off between performance and the domain (Yokoyama & Takahashi, 2010) when we tune the IDA-PBC.…”

Section: Simulationmentioning

confidence: 99%

Passivity-Based Nonlinear Stabilizing Control for a Mobile Inverted Pendulum

Yokoyama

Takahashi²

2011

Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics

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Mobile inverted pendulums (MIPs) need to be stabilized at all times using a reliable control method. Previous studies were based on a linearized model or feedback linearization. In this study, interconnection and damping assignment passivity-based control (IDA-PBC) is applied. The IDA-PBC is a nonlinear control method which has been shown to be powerful in stabilizing underactuated mechanical systems. Although partial differential equations (PDEs) must be solved to derive the IDA-PBC controller and this is a difficult task in general, we show that the IDA-PBC controller for the MIP can be derived solving the PDEs. We also formulate conditions which must be satisfied to guarantee asymptotic stability and show a procedure to estimate the domain of attraction. Simulation results indicate that the IDA-PBC controller achieves fast performance theoretically ensuring a large domain of attraction. We also verify its effectiveness in experiments. In particular control performance under an impulsive disturbance to the MIP are verified. The IDA-PBC achieves as fast transient performance as a linear-quadratic regulator (LQR). In addition, we show that even when the pendulum declines quickly and largely because of the disturbance, the IDA-PBC controller is able to stabilize it whereas the LQR can not.

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“…The advantage of IDA-PBC is that the Hamiltonian function can be implemented as an appropriate candidate for Lyapunov function in the stability analysis. IDA-PBC is a thoroughly well known control strategy for stabilisation of a wide class of mechanical systems such as those presented in [1,10,11].…”

Section: Introductionmentioning

confidence: 99%

Robust control approach for handling matched and/or unmatched uncertainties in port‐controlled Hamiltonian systems

Binazadeh

Karimi

Tavakolpour-Saleh

2019

IET cyber-systems robotics

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Stabilization of a Cart-Inverted Pendulum with Interconnection and Damping Assignment Passivity-Based Control Focusing on the Kinetic Energy Shaping

Cited by 7 publications

References 19 publications

Stabilization of a Mobile Inverted Pendulum with IDA-PBC and Experimental Verification

Stabilization of a Mobile Inverted Pendulum with IDA-PBC and Experimental Verification

Passivity-Based Nonlinear Stabilizing Control for a Mobile Inverted Pendulum

Robust control approach for handling matched and/or unmatched uncertainties in port‐controlled Hamiltonian systems

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