 Proceedings of Engineering and Technology Innovation , vol. 4, 2016, pp. 07 - 09 7 Performance Improvement of a Feedback Control System Using an Accelerometer-Enhanced Velocity Observer Yu-Sheng Lu * , Chung-Heng Lee Department of Mechatronic Engineering, National Taiwan Normal University, Taipei 106, Taiwan. Received 22 February 2016; received in revised form 19 March 2016; accept ed 16 April 2016 Abstract The paper shows how an acce lero meter - enhanced velocity estimator can be used to im- prove the tracking performance of a feedback control system. In contrast to conventional v e- locity estimators that use positional info rmation only, the accelero meter -enhanced velocity es- timator fuses the position sensor and the accel- erometer together to produce an improved ve- locity estimation. Expe rimental results are pre - sented to show the effectiveness of the accel- erometer-enhanced velocity estimator on im- proving the tracking performance of a linear motion stage. Keywor ds : Accelerometer, feedback control system, linear motion stage, veloc- ity estimator, velocity observer 1. Introduction A linear mot ion stage, shown in Fig. 1, is the e xperimental system, whose schematic is shown in Fig. 2. In the e xperimental system, a perma - nent-magnet synchronous ac motor is driven by a regulator current converter that receives a torque-producing command in the form of an a- log voltage fro m the DAC interface of a co n- trolle r core . The controlle r core is a DSP/ FPGA -based system with DIO, ADC and DAC interfaces. The FPGA is configured to interface with an optical linear encoder for p o- sition counting and velocity detection. Here, the velocity detection imple mented in the FPGA is based on the so-called inverse-time method (ITM) [1] that estimates velocity by measuring the time elapsed during two consecutive rising edges of a quadrature encoder signal. Moreover, the ADC interface in the FPGA acquires accel- eration from an accelerometer. Fig. 1 Photo of the experimental system Fig. 2 Schematic of the experimental system The DSP reads feedback informat ion on the acceleration, position and velocity (when the ITM is used) through the DSP interface in the FPGA, calcu lates velocity estimation and co n- trol algorith ms, and sends the control effort to the regulator current converter through the DAC interface. The output shaft of the motor is co n- nected to a ball screw that translates rotational motion of the rotor to linear motion of the pa y- load, on wh ich the accelero meter is mounted. In this paper, the position control of the payload is considered. * Corresponding aut hor. Email: luys@ntnu.edu.tw Proceedings of Engineering and Technology Innovation , vol. 4, 2016, pp. 07 - 09 8 Copyright © TAETI 2. Method The linear motion stage is used to evalu ate the performance of two veloc ity observers: one is an accelero meter-enhanced velocity estimator, the DCVO [2], and the other is the conventional, popular estimator using the inverse-time method (ITM). The plant is modeled as a second -order system described by  dubxaxax  12  (1) in which 857.4 2 a , 01 a , 11432b , x and u denote the plant’s output and input, re- spectively, and d denotes an uncertain input disturbance. The feedback controller is designed based on the Integral Variable - Structure Control (IVSC) law [3]. Define a switching function zceces 10   (2) where n c 2 0  , 2 1 n c  , and 0 0 zedtz t   . Fig. 3 Step response with the ITM Fig. 4 Step response with the DCVO Here, )( 000 1 10 ececz    and 30 n   . Let the IVSC law be     0 1 2 0 1 ˆˆ sgn( ) u x r c e c e c s x D r c e c e s                   (3) in wh ich n c  2 , 1ˆ b   , ˆ0.4   , 2 1ˆ ab   , 0 , and 1.0D . 3. Results and Discussion Fig. 5 Output error with a resolution of 20 m Fig. 6 Output error with a resolution of 5 m Two references are used in the following e x- periments: one is a step reference of 10 mm, and the other is a sinusoidal reference of 0.25 Hz. Figs . 3 and 4 show the step responses with the ITM and the DCVO, respectively. It is seen that the switching frequency of the control input associ- ated with the DCVO is much faster than with the ITM, meaning that the DCVO enables faster correction of output errors than the ITM. The upper subplot of Fig. 5 shows the error responses to the step reference, whereas the lower sub plot shows the error responses to the sinusoidal ref- erence. It is seen that compared with the ITM, the 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 m m Position 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.1 0 0.1 m m Error 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 m m /s Error dot 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.5 0 0.5 1 1.5 Time (s) V Control 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 m m Position 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.1 0 0.1 m m Error 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 m m /s Error dot 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.5 0 0.5 1 1.5 Time (s) V Control 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.1 -0.05 0 0.05 0.1 Time (s) m m ITM DCVO 0 0.5 1 1.5 2 2.5 3 3.5 4 -0.1 -0.05 0 0.05 0.1 Time (s) m m ITM DCVO 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.1 -0.05 0 0.05 0.1 Time (s) m m ITM DCVO 0 0.5 1 1.5 2 2.5 3 3.5 4 -0.1 -0.05 0 0.05 0.1 Time (s) m m ITM DCVO Proceedings of Engineering and Technology Innovation, vol. 4, 2016, pp. 07 - 09 9 Copyright © TAETI DCVO reduces the output error with the aid of an accelerometer. Moreover, in the case of regula- tion control, output precision is limited by the sensor resolution. In the subsequent experiments, the resolution of the pos itional sensor is reduced to 5 m. Like wise; the upper subplot of Fig. 6 shows the error responses to the step reference, whereas the lower subplot shows the error re- sponses to the sinusoidal reference. It can be clearly seen that the DCVO outperforms the ITM. Because of the advance of MEMS technology, accelerometers become cheap and ubiquitous, ma king the accelerometer-enhanced velocity estimator a cost-effective scheme with improved performance. 4. Conclusions In this paper, two velocity estimation schemes have been experimentally evaluated using the same IVSC law. The e xperimental results show that the DCVO enables higher-speed error cor- rection and leads to better tracking precision than the conventional estimator using the ITM. Acknowledgement The authors would like to thank the Ministry of Sc ience and Technology for their support of this research under Grants No. M OST 104-2221 -E-003-011-M Y2. References [1] J. S. Farrokh, H. Vincent, and C. S. J. Chen, “Discrete-time adaptive windowing for ve- locity estimation,” IEEE Trans . Contr. Syst. Technol., vol. 8, no. 6, pp. 1003-1009, 2000. [2] Y. S. Lu and S. H. Liu, “The design and imple mentation of an accelerometer-assisted velocity observer,” ISA Transactions, vol. 59, pp. 418-423, Nov. 2015. [3] J. H. Lee, “Highly robust position control of BLDDSM using an improved integral vari- able structure system,” Automatica, vol. 42, pp. 929-935, 2006.