Abstract
As the extension of traditional linear (or X) inverted pendulum (IP), X-Z IP is a multiple-input multiple-output (MIMO), underactuated, open-loop unstable, and nonlinear system. In the tracking control of the X-Z IP, the equilibrium point changes with the pivot position of the pendulum. This makes linear control theories have difficulties in realization of the tracking control for the pendulum. The underactuated feature of the pendulum makes the feedback linearization unsuitable to simplify the control design. With the present model of the X-Z IP, there is no way to realize the backstepping design. This paper gives a novel state transformation method for the X-Z IP. Through the state transformation, the block backstepping can be easily deployed in the controller design of the X-Z IP. The proposed controller can achieve the tracking control in the vertical plane. Simulation results certify the rightness and effectiveness of the proposed tracking controller.
Highlights
The traditional linear inverted pendulum (IP), which can be called X IP, is a typical test platform for different control strategies and is widely used by the researchers.As we know from the literature, before 2000, the research studies on the IP were mainly concentrated on the X IP
(3) In the state transformation and controller design, the state transformation and controller design is effective within a certain range of the parameter uncertainties and external disturbances. This brief paper extended the research on the X-Z IP, and the tracking control of the
(1) A novel state transformation method was proposed for the X-Z IP
Summary
The traditional linear inverted pendulum (IP), which can be called X IP, is a typical test platform for different control strategies and is widely used by the researchers. This brief paper mainly concentrates on the controller design for the X-Z IP. Only a few examples of literature can be found that concentrated on the tracking control of the X-Y or X-Z IP. According to the present literature as far as we know, there is no report on the tracking control of the X-Z IP with block backstepping. The backstepping requires that the control system under consideration is in the strict feedback form. The block backstepping will be adopted to solve the tracking control problem for the X-Z IP.
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