The 14th International Conference on Flexible Automation and Intelligent Manufacturing (FAIM2004)
Servo Control of a Pneumatic Muscle Actuator Po Wah...
The 14th International Conference on Flexible Automation and Intelligent Manufacturing (FAIM2004)
Servo Control of a Pneumatic Muscle Actuator Po Wah Chan and Gary M. Bone, Robotics and Manufacturing Automation Laboratory, McMaster Manufacturing Research Institute (MMRI). Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Introduction • Braided pneumatic muscle actuators (PMAs) are also known as “McKibben artificial muscles” although they were actually invented by Gaylord in 1958. • They have the advantages of high power to weight ratio and simplicity of design.
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Introduction (page 2) • Structure of a PMA: Inlet/Outlet Seal Pipe
End Cap
Air Flow End Plug
Rubber Inner Tube
Braided Fiber Shell
(image from Park and Meek, 1993)
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Introduction (page 3) • Mechanical principle: Braided Fibers (Pantograph Mechanism) Axial Contraction Force Air Pressure
• Although the early PMA were prone to fatigue failure the models sold by Festo are capable of millions of cycles. Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Introduction (page 4) • A PMA produces a unidirectional force. • The required antagonistic force can be supplied by a second PMA or other means. • Relatively few researchers have worked on the servo position control of PMAs. • Caldwell’s group at the University of Salford in the UK is the most active in this area. They do not use Festo’s PMA. Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
System Hardware 12 Bit ADC 24VDC Power Supply PC
Digital Output
Solid State Relay
Position Feedback Festo PMA
Air Supply Solenoid Valve
Figure 1: Hardware schematic.
Payload Mass
Linear Potentiometer Linear Slide
Gravity
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
System Hardware (page 2)
PMA fully extended Linear Potentiometer Payload Mass (23 kg)
• Extended length = 320 mm and Max. Stroke = 80 mm (%25) Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Plant Modeling • Required for design of model-based control algorithms. • Solenoid valve has 7 ms energize and 2 ms de-energize times. • Due to valve’s dynamics the PWM period and sampling period were both set to 20 ms. • Plant input, u, is the PWM duty cycle in %, and plant output, y, is the payload position in mm.
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Plant Modeling (page 2) • Started with a series of open-loop step input tests, approximated by first order models. Step Size (%)
gSS (mm / %)
τ RETRACT (s)
τ EXTEND (s)
50 60 70 80 90
1.7 2.1 1.9 1.7 1.5
2.1 1.9 1.5 1.2 0.7
0.3 0.5 0.7 1.0 1.1
• Speed of response is limited by the valve’s flow rate capacity. Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Plant Modeling (page 3)
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Plant Modeling (page 4) • Although the plant is nonlinear, the standard ARX model structure will be used: y ( k ) = − a1 y ( k − 1) − ... − an y ( k − n) + b0u (k − d ) + ... + bm u (k − d − m) + v(k )
• Standard LS parameter estimation minimizes the onestep-ahead (OSA) prediction errors: eP (k ) = y (k ) − yˆ (k ) where: yˆ (k ) = −a1 y (k − 1) − ... − an y (k − n) + b0u (k − d ) + ... + bmu (k − d − m)
• The multi-step-ahead (MSA) prediction for y(k) is: yˆ (k ) = − a1 yˆ (k − 1) − ... − an yˆ ( k − n) + b0u (k − d ) + ... + bm u (k − d − m) for k > n
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Plant Modeling (page 5) • Model-based controllers such as feedforward control and long-range predictive control use the model to predict many steps ahead in time. • A model estimated by minimizing the MSA prediction errors should result in improved controller performance. • We obtained this “optimized model” using the Matlab function fmins.
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Plant Modeling (page 6) • Data collected using filtered pseudo-random input sequence (N=200): Control (%)
100 80 60 40 20
0
0.5
1
1.5
2 2.5 Time (s)
3
3.5
4
0
0.5
1
1.5
2 2.5 Time (s)
3
3.5
4
Position (mm)
80 60 40 20 0 -20
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Sum of squared OSA prediction errors (mm2) 4.33 11.4
2.5
3
3.5
4
Sum of squared MSA prediction errors (mm2) 1,860 907
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Control Algorithm Design • Designed the following model-based controllers: – Extended PID control (EPID) – Feedforward (FF) – Generalized Predictive Control (GPC) – Iterative Learning Control (ILC)
• Each controller has only one parameter requiring manual tuning. • Planned a smooth position trajectory with Vmax = 60 mm/s and Amax = 400 mm/s2 Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
Experimental Results
Error (mm)
Position & Setpoint (mm)
• Using EPID controller: 40 20 0
Setpoint (mm) Position (mm) 0
1
1.5
2
2.5
20
emax = 12.7 mm
10 0 -10 0
Control (%)
0.5
0.5
1
1.5
2
2.5
0.5
1
1.5 Time (s)
2
2.5
80 60 40 0
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
3
Experimental Results (page 2)
Error (mm)
Position & Setpoint (mm)
• Using EPID plus FF controller: 40
0
0
0.5
1
1.5
2
2.5
4 2
emax = 3.2 mm emean = 1.7 mm
0 -2
Control (%)
Setpoint (mm) Position (mm)
20
0
0.5
1
1.5
2
2.5
0
0.5
1
1.5 Time (s)
2
2.5
80 60 40
Robotics and Manufacturing Automation Laboratory of the MMRI http://robotics.mcmaster.ca
3
Experimental Results (page 3) Result After Nine Learning Trials 40 Setpoint (mm) Position (mm)
