In this study, a control moment gyroscope is used as an actuator to stabilize the inverted pendulum. A control strategy is proposed to stabilize the inverted pendulum at the upright unstable equilibrium point and to maintain the gimbal angle as small as possible. Such a problem is formulated as a constrained H∞ disturbance attenuation problem and then transformed into solving linear matrix inequalities. The performance of the proposed controller is evaluated through simulation for linear and nonlinear cases. It is shown that the proposed state-feedback control strategy effectively stabilizes the inverted pendulum.
BaeHOhJ (2018) Biped robot state estimation using compliant inverted pendulum model. Robotics and Autonomous Systems108: 38–50.
2.
BalasGChiangRPackardA, et al. (2018) Robust Control Toolbox: User’s Guide. Massachusetts: MathWorks.
3.
ChenHGuoKH (2005) Constrained H∞ control of active suspensions: an LMI approach. IEEE Transactions on Control Systems Technology13(3): 412–421.
4.
DaiFGaoXJiangS, et al. (2015) A two-wheeled inverted pendulum robot with friction compensation. Mechatronics30: 116–125.
5.
HuangCYehT (2019) Anti slip balancing control for wheeled inverted pendulum vehicles. IEEE Transactions on Control Systems Technology28: 1042–1049.
6.
JinHYangDLiuZ, et al. (2015) A gyroscope-based inverted pendulum with application to posture stabilization of bicycle vehicle. In: Proceedings of the 2015 IEEE conference on robotics and biomimetics, Zhuhai, China, 6–9 December 2015, pp. 2103–2108. IEEE.
7.
KajitaSMorisawaMMiuraK, et al. (2010) Biped walking stabilization based on linear inverted pendulum tracking. In: 2010 IEEE/RSJ international conference on intelligent robots and systems, Taipei, Taiwan, 18–22 October 2010, pp. 4489–4496. IEEE
8.
KawajiriSMatunagaS (2017) A low-complexity attitude control method for large-angle agile maneuvers of a spacecraft with control moment gyros. Acta Astronautica139: 486–493.
9.
KimSKwonS (2017) Nonlinear optimal control design for underactuated two-wheeled inverted pendulum mobile platform. IEEE/ASME Transactions on Mechatronics22(6): 2803–2808.
10.
KumarMAKanthalakshmiS (2018) H∞ tracking control for an inverted pendulum. Journal of Vibration and Control24(16): 3515–3524.
11.
MashadiBGowdiniM (2015) Vehicle dynamics control by using an active gyroscopic device. Journal of Dynamic Systems, Measurement, and Control137(12): 1–12.
12.
PerezTBlankeM (2012) Ship roll damping controlAnnual Reviews in Control36: 129–147.
13.
PrasadLBTyagiBGuptaHO (2014) Optimal control of nonlinear inverted pendulum system using PID controller and LQR: Performance analysis without and with disturbance input. International Journal of Automation and Computing11(6): 661–670.
14.
RamirezDRAlamoTCamachoEF (2011) Computational burden reduction in min–max MPC. Journal of the Franklin Institute348(9): 2430–2447.
15.
SanjeewaSDAParnichkunM (2019) Control of rotary double inverted pendulum system using mixed sensitivity H∞ controller. International Journal of Advanced Robotic Systems16(2): 1–17.
16.
SprengerBKuceraLMouradS (1998) Balancing of an inverted pendulum with a SCARA robot. IEEE/ASME Transactions on Mechatronics3(2): 91–97.
17.
SunWGaoH, and KaynakO (2011) Finite frequency H∞ control for vehicle active suspension systems. IEEE Transactions on Control Systems Technology19(2): 416–422.
18.
TarbouriechSGarciaGGlattfelderAH (2007) Advanced Strategies in Control Systems with Input and Output Constraints. Springer-Verlag Berlin: Springer.
19.
TurnerMCPostlethwaiteI (2002) Output violation compensation for systems with output constraints. IEEE Transactions on Automatic Control47(9): 1540–1546.
20.
ViswanathanSPSanyalAKLeveF, et al. (2015) Dynamics and control of spacecraft with a generalized model of variable speed control moment gyroscopes. Journal of Dynamic Systems, Measurement, and Control, 137(7): 1–12.
21.
VotelRSinclairD (2012) Comparison of control moment gyros and reaction wheels for small earth-observing satellites. In: 26th annual AIAA/USU conference on small satellites, Utah, USA, 13–16 August.
