Manufacturer:      REX Controls (Pilsen, Czech Republic)
Brief description of the model
unstable mechatronic system for teaching and demonstration of automatic control algorithms
the motor-actuated rotary arm forces or suppresses the movement of a freely rotating pendulum to achieve the desired control objective
at the core of the model is the REX multiplatform industrial control system which processes sensor signals, implements control algorithms using a built-in block library and controls the motor
compatibility of the REX system with the MATLAB/Simulink program environment allows to test the proposed control algorithm in simulation using the mathematical model of the system
REX control system
open and scalable system suitable for embedded control; combines real-time control core with a top-layer host development (operator management) environment
the principal components of the host development environment (upper layer) are:
RexDraw – a built-in block editor for designing functional REX control system block schemes in form of .mdl files; can be replaced by Simulink with installed RexLib library
RexComp – compiler which transforms the application project's main file in the .mdl format into a binary .rex file, proprietary to the REX control system
RexView – diagnostic tool which provides detailed, hierarchical information about the block variables, real-time trends and task timing behavior
visualization tools – connect to the control system through an OPC interface
the structure of the target environment (lower layer) is composed of:
RexCore – real-time control core of the system, with the input/output drivers implemented as independent .dll files to allow modularity
the REX development tools were originally designed to work with the Windows operating system, as well as with industrial PCs with hard real-time operating system PharLap ETS through the PCI interface (I/O Advantech)
REX was revised following the incorporation of Ethernet Powerlink communication protocol (2009); after the development of the EplDrv driver, the REX control system was ported to the Alix platform, running under GNU/Linux environment with Xenomai hard real-time extension, separating the control core from B&R I/O modules in the process
Obr.1 REX control system structure
Laboratory model of the FPM-210/211 rotary inverted pendulum
one of the first models by REX Controls to implement the modified, Linux-based REX architecture
the model is composed of an arm rotating in the horizontal plane and an attached pendulum with the load concentrated at the end of the rod, which moves in a plane perpendicular to the horizontally-placed arm
control of the arm's horizontal rotation is provided by a servodrive which contains an AC brushless synchronous servodrive with a separate 1:5 planetary gearbox
human-machine interface of the system is represented by a touchscreen panel PC connected to a switchgear
the servodrive receives the information about the magnitude of the action signal through the Ethernet Powerlink communication protocol
the information about the angle deflection of the arm and pendulum, obtained from an IRC sensor and an absolute capacitory sensor respectively, is digitalized in the A/D converter, located in a remote I/O device, and passed to the RexCore, which operates on the ALIX platform (CPU board) with Linux and Xenomai installed
the control algorithm is realized by REX using a two-file configuration:
exec.mdl – the executive file which defines the target platform the configuration will be compiled for, sampling time (tick), input/output drivers oand the respective tasks of the control algorithm
xxx.mdl – a file which implements a control algorithm modeled by RexLib function blocks; every new control algorithm needs to be precompiled into a .rex file before it is downloaded into the RexCore and run
the available 3D visualization of the system was created as a Java application based on the open-source Java3D library : the displayed mobile 3D model follows the position of the laboratory model in real-time allowing to view the model from any angle
Obr.2 FPM-210/211 rotary pendulum system structure
the user is allowed to choose from the two available modes to work in:
demonstration mode - involves a predefined sequence of control procedures (pendulum swing-up, stabilization in the upright and downward equilibrium and tracking a predefined trajectory by the arm)
user control mode - lets the user choose the arm setpoint and the type of control procedure to be executed
Mathematical model of the FPM-210/211 rotary inverted pendulum
desired arm velocity
actual arm position - α
actual pendulum position - β
actual arm velocity - α'
the employed mathematical model is composed of 2 equations:
the servodrive velocity control loop, approximated by a first-order dynamic system, with the desired arm velocity as the input
the motion equation of the pendulum, given as a nonlinear relationship between the pendulum angle and the arm acceleration
Obr.3 Scheme of the mechanical design of the rotary pendulum model
all subsystems starting with Simulation_ are ignored by the RexComp compiler, i.e. the same control algorithm (a single file) can be employed in simulation (as a single file) and in generating a configuration .rex file for the target platform
Application of the laboratory model and simulation models of linear (classical) and rotary inverted pendulum systems in the research process
JADLOVSKÁ, S. – SARNOVSKÝ, J.: Nonlinear Control Design for Inverted Pendulum Systems Based on State-Dependent Riccati Equation Approach. Proceedings of the 5th International Conference on Applied Electrical Engineering and Informatics – AEI 2012, August 26 – September 2, 2012, Kiel, Germany, ISBN 978-80-553-1030-5 (AFC).
JADLOVSKÁ, S. – SARNOVSKÝ, J.: A Complex Overview of the Rotary Single Inverted Pendulum System. Proceedings of the 9th International Conference - ELEKTRO 2012, May 21-22, 2012, Žilina - Rajecké Teplice, Slovak Republic, pp. 305-310, ISBN: 978-1-4673-1178-6 (AFD).
JADLOVSKÁ, S.: Swing-up and Stabilizing Control of Classical and Rotary Inverted Pendulum Systems. Proceedings of the 12th Scientific Conference of Young Researchers – SCYR 2012, May 15, 2012, Herľany, Slovak Republic, pp. 38-41, ISBN: 978-80-553-0943-9 (AFD).
JADLOVSKÁ, S. – SARNOVSKÝ, J.: Classical Double Inverted Pendulum - a Complex Overview of a System. Proceedings of the IEEE 10th Jubilee International Symposium on Applied Machine Intelligence and Informatics – SAMI 2012, January 26-28, 2012, Herľany, Slovak Republic, pp. 103-108, ISBN: 978-1-4577-0195-5 (AFD).
JADLOVSKÁ, S. – SARNOVSKÝ, J.: An Extended Simulink Library for Inverted Pendula Modeling and Simulation. 19th Annual Conference Proceedings of the International Scientific Conference - Technical Computing Prague 2011, November 8, 2011, Congress Center - CTU Prague, Czech Republic, ISBN 978-80-7080-794-1 (AFC).
JADLOVSKÁ, S. – SARNOVSKÝ, J.: Matlab-Based Tools for Analysis and Control of Inverted Pendula Systems. Electrical Engineering and Informatics 2: Proceeding of the Faculty of Electrical Engineering and Informatics of the Technical University of Košice - Košice, FEEI TU, 2011. pp. 403-408, ISBN 978-80-553-0611-7 (AED).
JADLOVSKÁ, S. – JADLOVSKÁ, A.: Inverted Pendula Simulation and Modeling – a Generalized Approach. Proceedings of the 9th International Scientific – Technical Conference on Process Control – ŘÍP 2010, June 7-10, 2010, Pardubice University, Czech Republic, ISBN 978-80-7399-951-3 (AFC).
JADLOVSKÁ, S. – JADLOVSKÁ, A.: A Simulink Library for Inverted Pendula Modeling and Simulation. 17th Annual Conference Proceedings of the International Scientific Conference - Technical Computing Prague 2009, November 19, 2009, Congress Center - CTU Prague, Czech Republic, pp. 45, ISBN 978-80-7080-733-0 (AFC).