Modelling and Offset-free Predictive Control of the Parallel-Type Double Inverted Pendulum

Paul, Ager; Küçükdemiral, İbrahim Beklan; Bevan, Gerain

doi:10.1109/icsc57768.2022.9993951

Cited by 1 publication

(3 citation statements)

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“…while the gravitational and elastic forces vector, as well as the control inputs gain matrix are [25] G…”

Section: Partial Derivatives Of the Inertia Matrix Mmentioning

confidence: 99%

“…with K i , i = 1, 2, 3, 4 to be nonlinear functions of the angle variables of the parallel double inverted pendulum which are given by [25]…”

Section: Partial Derivatives Of the Inertia Matrix Mmentioning

confidence: 99%

“…However, little has been done so far for treatment of the associated nonlinear optimal control problem [20][21][22]. In this article a novel nonlinear optimal (H-infinity) control method is developed for the parallel double inverted pendulum, and is tested in three different forms of this system: (i) a model with four state variables and one control input, describing the dynamics of a cart with double inverted poles but without including the position of the cart [23], (ii) a model with six state variables and one control input, describing the dynamics of a cart with double inverted poles after including the position of the cart [24], (iii) a model with eight state variables and two control inputs, describing the dynamics of two separate cart and inverted pole systems which are connected through an elastic link [25].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear optimal control of the parallel double inverted pendulum

Rigatos

Pomares

Abbaszadeh

et al. 2023

Preprint

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The article proposes a nonlinear optimal control method for the dynamic model of the parallel double inverted pendulum. Three different forms of this system are considered: (i) two poles mounted on the same cart resulting into a model with four state variables and one control input, (ii) two poles mounted on the same cart resulting into a model with six state variables and one control input, (iii) two different cart-pole systems connected through an elastic link, resulting into a model with eight state variables and two control inputs. To implement the proposed nonlinear optimal control method the dynamic model of the parallel double pendulum undergoes approximate linearization around a temporary operating point which is updated at each sampling instance. This operating point is defined within each sampling period by the present value of the state vector of the parallel double inverted pendulum and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the parallel double inverted pendulum a stabilizing H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is also being solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion holds, which signifies robustness of the control method under model uncertainty and external perturbations. Moreover, under moderate conditions it is proven that the control loop of the parallel double inverted pendulum is globally asymptotically stable. To implement state estimation-based control the H-infinity Kalman Filter is used as a robust observer. The nonlinear optimal control scheme for the parallel double inverted pendulum achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

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“…while the gravitational and elastic forces vector, as well as the control inputs gain matrix are [25] G…”

Section: Partial Derivatives Of the Inertia Matrix Mmentioning

confidence: 99%

“…with K i , i = 1, 2, 3, 4 to be nonlinear functions of the angle variables of the parallel double inverted pendulum which are given by [25]…”

Section: Partial Derivatives Of the Inertia Matrix Mmentioning

confidence: 99%