Rotary inverted pendulum control using neuro-adaptive robust generalized dynamic inversion

Abstract

The objective of this research is to design a robust control system for trajectory tracking of the under-actuated Rotary Inverted Pendulum (RIP). The focus is on achieving semi-global asymptotic stability in the absence of knowledge about the RIP geometric and inertia parameters. The control design commences by formulating differential servo constraint dynamics (VCD) that encapsulates the control objectives for the RIP. The baseline generalized dynamic inversion (GDI) control law is derived by inverting the VCD for the control voltage input using the Moore–Penrose generalized inverse. To enhance robustness against modeling uncertainties and exogenous disturbances, a sliding mode control (SMC) element is integrated within the GDI control system, resulting in the robust GDI (RGDI) control system. Furthermore, an adaptive estimator that is based on Radial Basis Function Neural Networks (RBF-NN) is adopted to eliminate the dependency of the RGDI control system on the RIP mathematical model. The weighting matrices of the RBF-NN are updated with the aid of a Lyapunov control function. The proposed control system offers robust solution and guarantees semi-global asymptotic stability to the unstable equilibria of the RIP dynamics in the absence of a mathematical model. The proposed control system’s performance is evaluated through computer simulations and experimental tests on a real RIP system. Comparative analyses with traditional SMC and linear quadratic control methodologies are conducted to show the effectiveness of the proposed approach.

Keywords

robust generalized dynamic inversion adaptive control radial basis functions neural networks Lyapunov stability sliding mode control

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References

Abbas

Pan

Raheem

, et al. (2022) Real-time robust generalized dynamic inversion based optimization control for coupled twin rotor mimo system. Scientific Reports 12(17852): 17852.

Abdullah

Amin

Iqbal

, et al. (2021) Swing up and stabilization control of rotary inverted pendulum based on energy balance, fuzzy logic, and LQR controllers. Measurement and Control 54(9-10): 1356–1370.

Ahmad

Shafiq

(2020) Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders. Automatika: Journal for Control, Measurement, Electronics, Computing and Communications 61(3): 396–414.

Ahmad

Saaban

Ibrahim

, et al. (2015) A research on adaptive control to stabilize and synchronize a hyperchaotic system with uncertain parameters. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 5(2): 51–62.

Ansari

Bajodah

(2017) Robust launch vehicle’s generalized dynamic inversion attitude control. Aircraft Engineering & Aerospace Technology 89(6): 902–910.

Ansari

Bajodah

(2018) Quadrotor motion control using adaptive generalized dynamic inversion. In Annual American Control Conference (ACC). IEEE, 4311–4316.

Ansari

Bajodah

(2018) Robust generalized dynamic inversion based control of autonomous underwater vehicles. Proceedings of the Institution of Mechanical Engineers - Part M: Journal of Engineering for the Maritime Environment 232(4): 434–447.

Ansari

Bajodah

(2019) Launch vehicle ascent flight attitude control using direct adaptive generalized dynamic inversion. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233(11): 4141–4153.

Ansari

Bajodah

(2019) Autonomous underwater vehicles attitude control using neuro-adaptive generalized dynamic inversion. IFAC-PapersOnLine 52(29): 103–109.

10.

Ansari

Bajodah

Hamayun

(2019) Quadrotor control via robust generalized dynamic inversion and adaptive nonsingular terminal sliding mode. Asian Journal of Control 21(3): 1237–1249.

11.

Ansari

Bajodah

Kada

(2019) Development and experimental investigation of a quadrotor’s robust generalized dynamic inversion control system. Nonlinear Dynamics 96(2): 1541–1557.

12.

Ansari

Bajodah

Kada

(2019) Nonlinear robust generalized dynamic inversion based homing guidance and control of aerial interceptors. IFAC-PapersOnLine 52(12): 219–226.

13.

Bajodah

Hodges

Chen

(2005) Inverse dynamics of servo-constraints based on the generalized inverse. Nonlinear Dynamics 39(1-2): 179–196.

14.

Ben-Israel

Greville

(2003) Generalized Inverses: Theory and Applications. Berlin: Springer Science and Business Media, Vol. 15.

15.

Greville

(1959) The Pseudoinverse of a rectangular or singular matrix and its application to the solution of systems of linear equations. SIAM Review 1(1): 38–43.

16.

Hall

Romano

Cristi

(2010) Quaternion feedback regulator for large angle maneuvers of underactuated spacecraft. In Proceedings of the 2010 American Control Conference, Baltimore, MD, June 30–July 2 2010, pp. 2867–2872, The American Control Conference (ACC 2010).

17.

Hameduddin

Bajodah

(2012) Nonlinear generalised dynamic inversion for aircraft manoeuvring control. International Journal of Control 85(4): 437–450.

18.

Hamza

Yap

Choudhury

, et al. (2019) Current development on using rotary inverted pendulum as a benchmark for testing linear and nonlinear control algorithms. Mechanical Systems and Signal Processing 116: 347–369.

19.

Howimanporn

Chookaew

Silawatchananai

(2020) Comparison between PID and sliding mode controllers for rotary inverted pendulum using PLC. In 4th International Conference on Automation, Control and Robots. IEEE, 122–126.

20.

Kada

Ansari

Bajodah

(2020) Highly maneuvering target interception via robust generalized dynamic inversion homing guidance and control. Aerospace Science and Technology 99: 105749.

21.

Khalil

(1996) Nonlinear Systems. New Jersey, USA: Prentice-Hall.

22.

Mehedi

Ansari

Bajodah

, et al. (2020) Underactuated rotary inverted pendulum control using robust generalized dynamic inversion. Journal of Vibration and Control 26(23-24): 2210–2220.

23.

Moreno-Valenzuela

Aguilar-Avelar

(2018) Feedback linearization control of the furuta pendulum. In Motion Control of Underactuated Mechanical Systems. Springer, 69–92.

24.

Nguyen

Kim

, et al. (2020) Fuzzy-based super-twisting sliding mode stabilization control for under-actuated rotary inverted pendulum systems. IEEE Access 8: 185079–185092.

25.

Prado

Herrera

Menendez

(2020) Intelligent swing-up and robust stabilization via Tube-based nonlinear model Predictive control for a Rotational inverted-pendulum system. Revista Politecnica 45(1): 49–64.

26.

Quanser (2012) Inverted Pendulum Experiment-SRV02 RTOPEN User Manual Quanser Inc. Ontario, Canada.

27.

Shiriaev

Freidovich

Robertsson

, et al. (2007) Virtual-holonomic-constraints-based design of stable oscillations of furuta pendulum: Theory and experiments. IEEE Transactions on Robotics 23(4): 827–832.

28.

Udwadia

Kalaba

(1996) Analytical Dynamics: A New Approach. Cambridge, UK: Cambridge University Press.

29.

Nguyen

, et al. (2020) Back-stepping control for rotary inverted pendulum. Journal of Technical Education Science 59: 93–101.

30.

Nguyen

VDH

Duong

, et al. (2023) Combining passivity-based control and linear quadratic regulator to control a rotary inverted pendulum. Journal of Robotics and Control, 4(4): 479–490.