Mathematical Model Analysis and Control Algoritms Design based on State Feedback Method of Rotary Inverted Pendulum

ABSTRACT

XZ-type rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ- rotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Matlab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.

KEYWORDS: Rotational Inverted Pudulem, Mathematical Model, State Feedback, Simulation, Debugging

INTRODUCTION

Rotary Inverted Pendulum

Inverted pendulum is typical multi-variable, nonlinear non-minimum-phase, unstable and underactuated system[1]-[5]. XZ- rotary inverted pendulum system uses DSP as the controller, and it has independent ability to complete realtime control algorithms without the computer; it also can complete computer cont rol by RS-232C serial communication interface, and on-line control algorithm can be debugged. DSP, power supply and motor drive are all installed in the chassis. The figure 1 shows the overall structure diagram of the system.

Figure 1: The Overall Structure Diagram of the XZ- Rotary Inverted Pendulum System

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DSP controller is the core control device; it can complete some functions such as data transfer, A / D, D / A conversion, computation, data processing etc. The executing agency of system is the DC torque motor driven by a dedicated drive circuit; it can control motion of inverted pendulum. Measurement feedback components are the two potentiometers used measure the angle signal of the pendulum and arm. Drive power.

Working Principle of the System

The spiral arm is drive by the DC torque motor, and it can rotate around the vertical plane that is perpendicular to motor axis. The pendulum and spiral arm are connected by activity shaft axis of a potentiometer, and the pendulum can rotate around shaft axis in the vertical plane that is perpendicular to the spiral arm. The two angular signals displacement can be measured by the potentiometers (one is lead angle between the spiral arm and the vertical line, another is the relative angle between the spiral arm and the pendulum), and they as two outputs of system t are sent to DSP controller. The angular velocity signal can be obtained by the differential of the angular displacement, and then using some state feedback control algorithm to calculate the control law is provided to the drive circuit after transformed into voltage signal, the signal is used to drive DC torque motor, at last, the arm's movement is achieved by the pendulum rotation driven by motor, working principle is shown as following figure 2, 3.

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Figure 2: Structure Block Diagram of the XZ- Rotary Inverted Pendulum System

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1 The Spiral Arm 2 The Pendulum 3 Potentiometers

4 DC Torque Motor 5 Frame 6 Chassis 7 Power Switch

Figure 3: Mechanical Structure Diagram of the XZ- Rotary Inverted Pendulum System

Introduction about Processing Software

Running DSP.exe, following figures 4, 3 will appear. Through this dialog, we can set up and change all parameters except for parameters of “running mode”. Therefore “running mode” can be changed only when system is stopping, else accident may be happened.

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Figure 4: Main Interface of Processing Software

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Figure 5: “Setting”Interface of Processing Software

Parameter settings include the following three aspects:

Running Mode

Control Mode: System control and data processing are done by the computer, and the sampling and output are achieved by the DSP using serial communication.

Monitor Mode: System control is completed by DSP; the computer is just used for observation and preservation of data.

Control Mode (User-Defined): When the users design their control algorithms, experimental control is done in this mode; system control and data processing are done by the computer, and the sampling and output are achieved by the DSP using serial communication..

Basic Setting

It is used to set the hardware parameters, including motor full capacity voltage, dead voltage, which generally do not need to change. The other is adjusting zero of the pendulum and the spiral arm, when the accident collision has happened, you may need to adjust them. When the system is input values, the pendulum or the spiral arm will bring out corresponding shift.