A Mitsubishi HC-KFS73 DC servo motor is used as the main actuator in the system. The DC servo motor is symmetrical loaded as shown in Fig. 2-1. The servo plant is consisted of a servo driver and servo motor. While the load being symmetrical, the plant can be regarded as a second-order linear system with one pole of 0 if the output is position, first-order if the output is velocity. Letting the system dynamics be
bu x a
x , (2) where a and b are plant parameters and u is the control input, x , x and x are system states being position, velocity and acceleration.
The motor is paired with an encoder of 262144 p/rev resolution, the encoder signal is sent to the driver and is then output in an A/B phase form from the driver. The DC servo is used in torque command mode, with an input range of -5.5 ~ 5.5 V.
Fig. 2- 1Experimental setup of symmetrically loaded DC servo
Symmetrically loaded motor Driver
8 2.2 System hardware structure
The experimental system’s hardware structure is shown in Fig. 2-2. Aside from the plant, a controller core and personal computer are used. The controller core is mainly consisted of a Texas Instruments TMS320C6713 development starter kit and a FPGA daughter board. The FPGA daughter board is connected to the DSP through a data bus and has a D/A converter interface and differential line receiving interface for receiving the driver’s A/B phase signal. The control effort is calculated by the DSP and transferred to the FPGA and sent through the D/A interface into the driver, the driver receives the encoder data of the motor and outputs the A/B phase signal to the FPGA daughter board’s differential line receiver, the A/B phase data is separately counted for the position and velocity signal in the FPGA and then sent to the DSP, the DSP uses the feedback data for control to fulfill the closed loop. When the experiments are finished, the DSP sends the experiment data through a USB interface to the personal computer for analysis.
Fig. 2- 2 Block diagram of system hardware structure
The hardware of the controller core is shown in Fig. 2-3, the bottom board is the Texas Instruments TMS320C6713 development starter kit and the top board is the FPGA daughter board. The DSP and FPGA have a synced clock of 90 MHz while operating
D/A Driver Motor
Controller core
Plant Xilinx
FPGA
Diff. line receiver Texas Instruments
6713DSP Personal
computer
Encoder A/B phase
signal Control
signal Experiment
data
9 with a sampling period of 9.102105s.
Fig. 2- 3 DSP and FPGA controller core of system
10 2.3 System identification and modeling
The DC servo can be assumed as a linear system, thus by using a swept-sine method, the plant model can be found. The swept-sine interface is shown in Fig. 2-4, a National Instruments PXI-4461 Dynamic signal analyzer (DSP) is used for the signal generation and receiving, the generated sinusoidal signal is directly input into the driver as a control signal and the A/B phase signal is sent to the controller core for velocity estimation, the estimated velocity is then output through a D/A converter on the controller core and sent back to the DSA as the output of the system.
Fig. 2- 4 Block diagram of swept-sine system identification method
The swept-sine procedure is started from 0.02 Hz and ended at 50 Hz. A first order curve fit of the data is performed to find the transfer function of the system, the data points and curve fitting results are shown in Fig. 2-5. The transfer function of the curve fit result is
1642 . 0
5 . 180 )
V (
) rad/s (
s u
. (3)
Controller core Plant
(Driver + motor) National Instruments PXI-4461
Generated swept-sine output
Input den num
A/B phase Velocity
signal
11
But due to the pole of the system being very small and hard to find by a swept-sine method, a time-optimal control (TOC) of a second-order plant is used for further identification of the system.
10−1 100 101 102 103 curve fitting result
10−1 100 101 102 103 curve fitting result
Fig. 2- 5 Swept-sine and curve fitting results of DC servo
The TOC of a second-order system as in [25] is used due to its model based properties and also easy to observe through the phase plane. The switching property of the control method is
the TOC of a second-order system in which
kSO
12 By adjusting the control output of the controller to
)}
u being the output of the controller, the plant and controller can be viewed as TOC of second-order and a double integrator. Due to this method being very sensitive to plant parameters, the parameter adjustment can be done through experiments. Fig. 2-6 is the second-order TOC using the plant parameters of the curve fit results, it can be seen that the reaching near the origin of the phase plane isn’t ideal. Thus, by adjusting the parameters of the system to
001642
making the pole of the plant 100 times smaller, the reaching near the origin of the phase plane is more ideal and the system states converge to zero more correctly as shown in Fig.
2-7. TOC switching curve
Fig. 2- 6 TOC of a second-order plant with curve fit plant parameters
13
−2 −1.8 −1.6 −1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0
1 2 3 4 5 6 7 8
error error dot
system states TOC switching curve
Fig. 2- 7 TOC of a second-order plant with adjusted pole
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