The Design of Fuzzy Adaptive PID Controller of Two-Wheeled Self-Balancing Robot

Transcription

1 The esign of Fuzz Adaptive PI Controller of Two-Wheeled Self-Balancing Robot Conging Qiu and Yibin Huang Abstract A two-wheeled self-balancing robot sstem is developed and the hardware sstem mainl consists of a controller of TMS3LF47 SP, a main sensor of Mio-x AHRS module, and other bargain components. The traditional linear controllers have a number of crucial flaws in controlling of two-wheeled self-balancing robot, such as long settling time and large overshoot. Therefore, we conducted further research on the fuzz control method, designed a fuzz adaptive PI controller with an improved structure, and simplified its algorithm process. Simulation results demonstrate that the fuzz adaptive PI controller has a shorter settling time and smaller overshoot than the traditional linear controller and it is more suitable for large time dela, multi-parameter, high-order, strong coupling, and nonlinear two wheel self-balancing robot sstem control. Index Terms Intelligent robot, two-wheeled self-balancing robot, fuzz logic, fuzz PI, adaptive, MATLAB simulation. II. ROBOTIC YNAMIC MOEL The two-wheeled self-balancing robot is shown as Fig. and its dnamics analsis is referred to [3]. Its state-space model is expressed as () shows. Meanwhile, the transfer function can be obtained from (3). Fig.. The model of two-wheeled self-balancing robot. I. INTROUCTION With the advance of technolog in two-wheeled self-balancing robots, man researchers have sought to focus on this area. While the majorit of commercial applications of two-wheeled self-balancing robots in the China s maret, we use special components from foreign countries, which are advanced but experience, resulting an unacceptable high cost [], []. Therefore, man efforts have been made to design a robot with cheap materials and then universalize it. To exploit the running gear of AROBOT teaching robot, which belongs to Institute of Automation, Chinese Academ of Sciences, a two-wheeled self-balancing robot is presented in this paper. This research aims to reduce the cost of two-wheeled self-balanced robots, especiall for the researchers who have been devoted to the application development of robots. The e of two-wheeled robots stabilit is to choose an appropriate control algorithm. In this paper, the deficienc of linear PI control, the selection of fuzz adaptive PI controller and the modification of control algorithm based on actual demand are determined, which are based on a complete analsis. Finall, simulation is performed to evaluate the method s feasibilit to control the two-wheeled self-balancing robots. The results show that the method has improved the robustness. Manuscript received Jul, 4; revised September 5, 4. Conging Qiu is with the Beijing Ke Laborator of Traffic Engineering, Beijing Universit of Technolog, Beijing, China ( qiuconging@gmail.com). Yibin Huang is with the Institute of Automation, Chinese Academ of Sciences, China ( @qq.com). x x x.757 x.8 = u () x x x () As ( ).879 Gs () (3) U ( s) s x, x,,, and u stand for robot s location, velocit, angle, angular velocit and controlling force, respectivel [3]. According to the actual sampling time T=.5s, we discretized the robotic transfer function model and then the robotic discrete transfer function was obtained as follow. Gz ( ) 6.75z.349z.75 z.z B conducting the Z inverse transformation for discrete transfer function, the difference equation of output angle and input control of controlled object are obtained. ( ). ( ) ( - ) 6 [.75 u( ).349 u( -).75 u( - ) ] In order to verif the feasibilit of the control algorithm, we performed a number of simulations in the MATLAB environment to the sstem, which was developed based on equations mentioned above. (4) (5) OI:.7763/IJIEE.5.V

2 III. EFICIENCY OF LINEAR CONTROLLER Reference [3] has introduced LQR, PI and etc. methods to control the robotic balance. The core algorithm of controlling the balance of robot, in essential, is PI algorithm or the improved PI control algorithm. Firstl, we conducted the experiment of discrete simulation with PI controller. Fig. shows the results obtained with the PI parameters K P =497.69, K I =8, K =94.3. With such PI parameters, the settling time of PI algorithm is too long. Therefore, it doesn t meet the requirement of effectiveness of real-time control of robotic balancing and it is demanded to shorten settling time b adjusting PI parameters. As shown in Fig. 3, after adjusting PI parameters to K P =497, K I =38, K =4, settling time T s =.35s, overshoot MP=86.7%. Large overshoot and integral oscillation after overshooting must lead poor control effect of robotic sstem. Therefore it is crucial to decrease the sstem s overshoot. The common method of PI controller to decrease overshoot usuall includes the means to reduce the scale factor, integral separation, and windup processing or increase the differential parameters etc [4] Fig.. Robot s PI control step response Fig. 3. Step response of increased PI integral control. If decreasing the proportionalit coefficient to reduce overshoot, sstem response will be slower. Furthermore, it ma not be able to achieve the reduction in overshoot, because when robot eeps in balance, its tilt angle generall doesn t exceed ± 3. Integral separation algorithm isn t applicable. Although integral windup can reduce overshoot, it weaens the capacit of integral departure tracing. Enlarging differential parameters can reduce overshoot, but the parameters are liel triggered to be oversized; and consequentl the sstem friction will be too large to bring a faster response to the sstem. In addition, exaggerated differential parameters will introduce extra speed noise to the sstem. In Fig. 4, the effect of controlling robot is disappointing, because it restricts integral amplitude, decreases proportionalit coefficient, and increases differential coefficient etc. Therefore, it is urgent to adjust the parameters of linear PI controller to guarantee that the response has a small overshoot. Fig. 4. Effect of reducing the overshoot b conventional methods. IV. ESIGN OF FUZZY SELF-AAPTIVE PI CONTROLLER Referred to fuzz logic control, it is a computer-based digital control technolog based on fuzz set theor, fuzz linguistic variables and fuzz logic [5], [6]. A PI controller is liel to cause some problems, such as large overshoot, depth integral saturated and points oscillation near the equilibrium point. The deficienc of PI controller can be fixed b appling fuzz control. Fuzz PI algorithm, combined PI theor with fuzz control theor, can easil control the balance of two-wheeled robot according to the expertise. Thus, in comparison to the traditional algorithms, smaller oscillation, faster response and better stabilit can be realized b the fuzz control due to the fact that the fuzz rules are rather similar to human cognitive level. Fuzz adaptive PI control is adaptive [7], [8]. In general, this method uses fuzz control algorithm to adjust PI parameters b means of fuzz reasoning to the current values of controlling departure and error rate. And, the algorithm finall meets the requirements of parameters of different e and ec ranges [9]. Mamdani fuzz controller shown in Fig. 5 is referred to the actual needs in MATLAB structure. There are two inputs and three outputs. The Mamdani fuzz reasoning method adopted has 49 fuzz rules in total. Among them, the fuzz approach is fuzz single value, the defuzzification method is average gravit. The output surface of fuzz controller is shown as Fig. 6 to Fig. 8. Compared to the initial algorithms, it has smoother fuzz surface; and the effect of fuzz controller is better. PI parameter group is K P =5, K I =5, K =4. According to controlling the surface shape, or sstem step response curve (Fig. 9), we adjust the quantization factor, the scaling factor, fuzz space partition or fuzz rules of fuzz controller in the simulation process. In Fig. 9, we set the fuzz PI sstem with parameters Ts=.75s, overshoot MP=38.7%. And, the simulation results show that this settling time has faster step response speed and smaller overshoot. Moreover, it is shorter than the one of classic PI control sstem, whose T s =.35s. Meanwhile, its overshoot is much less than the latter one, which is 86.7%. It proves that dnamic performance of fuzz control sstem is better than the classic PI control sstem. However, due to the integral hsteresis, the hsteresis of sstem overshoot is also too large. 94

3 Fig. 5. Fuzz controller structure. Fig.. Integral-time curve of fuzz control sstem. V. IMPROVEMENT OF FUZZY SELF-AAPTIVE PI CONTROLLER The output of fuzz PI controller is u( ) ( K K ) e( ) K e( j) P P I j ( K K )[ e( ) e( )] (6) Fig. 6. The output ΔKP surfaces of fuzz controller. Fig. 7. The output ΔKI surfaces of fuzz controller. I e( j) Its integral term j must have hsteresis. The rise time of fuzz PI control sstem is T r =.8s, and sstemic error passes through the equilibrium point again. The scope-time curve of integral term is shown in Fig.. When t =.75s, integral term passes through zero point to become negative. The hsteresis time is τ=t -Tr=.47s. Integral term hsteresis leads to large overshoot. Thus it is necessar to improve integral structure to ensure that the integral approach is more flexible and the hsteresis is weaer. The improved input of the sstem is u( ) ( K K ) e( ) K e( j) P P I j ( K K )[ e( ) e( )] I KIe( j) Its integral term j is flexible. Fuzz logic controller adjusts the value of ΔK I to what can meet the requirement. Meanwhile, the changed integral speed decreases its integral hsteresis and plas a similar role such as integral separation when the integration is not required. As shown in Fig., the time of fuzz control sstem after being improved is T r =.9s, settling time T s =.485s, overshoot value MP=33.8%. The improved integral-time curve is shown in Fig.. Integral term gets a zero crossing when t =.59, and hsteresis time τ=t -T r =.3s. (7) Fig. 8. The output ΔK surfaces of fuzz controller Fig. 9. Step response curve of fuzz control sstem. Fig.. Step response of improved structure before and after. Hsteresis time is shorter and the maximum value ahead to 95

4 t is smaller than before. The not onl help reduce sstem overshoot, but also shorten the convergence time. And it leads settling time of the improved sstem to be shorter, and overshoot to be smaller. The result proves that the method of an improved control sstem is better than the one of a fuzz PI sstem. significantl shorter and overshoot is smaller to a certain extent than before. It proves the feasibilit of replacing fuzz reasoning process with a loo-up table and that the improved integration sstem structure is better than linear integral sstem. Fig.. Integral-time curve of improved structure before and after. Fig. 3. Step response of fuzz PI sstem b loo-up table method. Fuzz logic controller algorithm is complex. It is hard to code the algorithm if directl b the program of C language, because there are too man parameters in fuzz controller and flexible structure. In addition, calculation and memor space of such method is too large to be available for low-frequenc, small-capacit controller. The fuzz controller uses fuzz logic in reasoning process, but each certain input onl corresponds to one certain output in the same fuzz sstem. Thus, we used the Matlab platform to program an appropriate controller. B replacing the fuzz reasoning process b approximation, the loo-up table method, reasoning process can be shortened in terms of processing time. Furthermore, this method has good portabilit in engineering. We mae approximate simplification to above improved control sstem structure before and after. The input e is approximate to 6 equidistant points and input ec to 5 equidistant points, and thus a two-dimensional table of 6 5 can be generated. Each element in the table contains the value of ΔK P, ΔK I and ΔK, which are corresponding to the respective input. The result in Fig. 3 shows an example of simulated loo-up table. The overshoot and settling time of fuzz PI control sstem, which are obtained b loo-up table, are respectivel that MP=47.% and T s =.445s. After structural improvement, MP=4% and T s =.s. Table method, to some extent, lows the sstem ambiguit and larges the overshoot. After the sstem s structural improvement, settling time is VI. CONCLUSION This research wor taes advantage of cheap components to design a two-wheeled self-balancing robot sstem. Considering the deficienc of the LQR and PI controller, this paper mainl studies the fuzz adaptive PI controller to further improve the controlling performance of the robot. Aiming at the shortage of long settling time and large overshoot of the linear PI control method, a fuzz adaptive PI controller is designed, which is suitable for controlling a two-wheeled self-balancing robot based on the simulation results. B means of analzing the hsteresis of integral term, we improved the integral structure of fuzz PI controller. On the basis of concrete analses of robot sstem, we replaced the fuzz inference process method with the loo-up table one. The MATLAB simulation results show that, the improved control sstem integration structure can be further shortened the robot settling time and reduces the sstem overshoot, and that self-balancing control is more suitable for the robot. Moreover, the feasibilit of loo-up table method is verified. Calculation amount of the control method in this paper is small, and the design process is simple, which is able to improve the oscillation phenomenon of a two wheeled robot. This technolog is promising in wide application prospect. REFERENCES [] J. Wu, W. Zhang, and S. Wang. (October ). A two-wheeled self-balancing robot with the fuzz PI control method. Mathematical Problems in Engineering. [Online]. Available: [] H. G, Nguen. J. Morrell, K.. Mullens, A. B. Burmeister, S. Miles, N. Farrington, and. W. Gage, Segwa robotic mobilit platform, in Proc. 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5 Conging Qiu was born in Guangxi Province, China, on March 8, 993. She is an undergraduate student of Beijing Universit of Technolog, Beijing, China in. Her major fields of stud are following: automatic, and intelligent transportation. Her publication includes: B. G. Zheng, Y. B. Huang, & C. Y. Qiu, LQR+ PI Control and Implementation of Two-Wheeled Self-Balancing Robot, in Applied Mechanics and Materials, vol. 59, pp , August, 4. Yibin Huang was born on Jul 8, 99. He is a Ph student of Institute of Automation, Chinese Academ of Sciences in 4. He was interested in the following fields: automatic, robotics and intelligent control. His recent publications is: B. G. Zheng, Y. B. Huang, & C. Y. Qiu, LQR+ PI Control and Implementation of Two-Wheeled Self-Balancing Robot, in Applied Mechanics and Materials, vol. 59, pp , August, 4. 97