Backstepping Linear Quadratic Gaussian Controller Design for Balancing an Inverted Pendulum

This paper presents a Backstepping controller for five degrees of freedom Spherical Inverted Pendulum. Since the system is nonlinear, unstable, underactuated and MIMO and has a nonsquare form, the classic control design cannot be applied to control it. In order to remedy this problem, we propose in this paper a new method based on hierarchical steps of the Backstepping controller taking into a count the nonlinearities that cannot be neglected. Furthermore, a Linear Quadratic Regulator controller and LQR + PID based on the linearized system model are also designed for performance comparison. Finally, a simulation study is carried out to prove the effectiveness of proposed control scheme and is validated using the virtual reality environment that proves the performance of the Backstepping controller over the linear ones where it brings the pendulum from any initial condition in the upper hemisphere while the base is brought to the origin of the coordinates.

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Stability Robustness of LQ and LQG Active Suspensions

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2900666 ◽

1994 ◽

Vol 116 (1) ◽

pp. 123-131 ◽

Cited By ~ 36

Author(s):

A. G. Ulsoy ◽

D. Hrovat ◽

T. Tseng

Keyword(s):

Controller Design ◽

Active Suspension ◽

Point Of View ◽

Linear Quadratic ◽

Linear Quadratic Gaussian ◽

Active Suspensions ◽

Quarter Car Model ◽

Stability Robustness ◽

Trade Offs ◽

Two Degree Of Freedom

A two-degree-of-freedom quarter-car model is used as the basis for linear quadratic (LQ) and linear quadratic Gaussian (LQG) controller design for an active suspension. The LQ controller results in the best rms performance trade-offs (as defined by the performance index) between ride, handling and packaging requirements. In practice, however, all suspension states are not directly measured, and a Kalman filter can be introduced for state estimation to yield an LQG controller. This paper (i) quantifies the rms performance losses for LQG control as compared to LQ control, and (ii) compares the LQ and LQG active suspension designs from the point of view of stability robustness. The robustness of the LQ active suspensions is not necessarily good, and depends strongly on the design of a backup passive suspension in parallel with the active one. The robustness properties of the LQG active suspension controller are also investigated for several distinct measurement sets.

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Attitude and Altitude Controller Design for Quad-Rotor Type MAVs

Mathematical Problems in Engineering ◽

10.1155/2013/587098 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 5

Author(s):

Wei Wang ◽

Hao Ma ◽

Min Xia ◽

Liguo Weng ◽

Xuefei Ye

Keyword(s):

Attitude Control ◽

Controller Design ◽

Sliding Mode ◽

Micro Air Vehicles ◽

Triaxial Accelerometer ◽

Linear Quadratic ◽

Linear Quadratic Gaussian ◽

Constant Altitude ◽

The Military ◽

Rotor Type

Micro air vehicles (MAVs) have a wide application such as the military reconnaissance, meteorological survey, environmental monitoring, and other aspects. In this paper, attitude and altitude control for Quad-Rotor type MAVs is discussed and analyzed. For the attitude control, a new method by using three gyroscopes and one triaxial accelerometer is proposed to estimate the attitude angle information. Then with the approximate linear model obtained by system identification, Model Reference Sliding Mode Control (MRSMC) technique is applied to enhance the robustness. In consideration of the relatively constant altitude model, a Linear Quadratic Gaussian (LQG) controller is adopted. The outdoor experimental results demonstrate the superior stability and robustness of the controllers.

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