Servo controller design and fault detection algorithm for speed control of conveyor system

Nội dung text: Servo controller design and fault detection algorithm for speed control of conveyor system

1. SERVO CONTROLLER DESIGN AND FAULT DETECTION ALGORITHM FOR SPEED CONTROL OF CONVEYOR SYSTEM Nguyen Trong Hai HUTECH Institute of Engineering, Ho Chi Minh City University of Technology (HUTECH) ABSTRACT This paper proposes a servo controller design and fault detection algorithm for speed control of conveyor system (CS). Firstly, modeling for a CS is described. Secondly, the robust servo controller based on polynomial differential operator is applied to track the trapezoidal velocity profile reference input. Thirdly, a fault detection algorithm based on Extended Kalman Filter (EKF) is proposed. From the EKF, the estimated angular velocity indicates the encoder failure. The estimated friction indicates the mechanical failure Fault isolation is obtained by the friction bound. Finally, the simulation and experimental results are shown to verify the effectiveness of the proposed algorithm. Keywords: Fault detection, Internal model principle, Kalman Filter, Servo system, Speed control. 1. INTRODUCTION Conveyors are material handling devices not only to transport loads/units but also to sort or store them temporarily. Most AC motor drives have used PI control [1] but difficult for applying to obtain sufficiently high performance in the tracking application. To satisfy the tracking requirements, huge amount of algorithms were proposed by researchers [2]–[5]. However, the transient performances are always unsatisfactory. To solve this problem, Kim, S. B. et al. [6-7] proposed a new concept of servo controller design method by introducing a polynomial differential operator. In this paper, a robust servo controller proposed by Kim, S. B. et al [7] is applied for speed control of a CS. The experimental results of the proposed servo controller are compared to the conventional PI controller and MRAC controller. Since the CS work automatically, their safety is considered. In order to maintain the conveyor system, several features such as energy consumption, output, temperature, vibrations, belt speed etc. might be monitor. The fault detection algorithm helps user to detect faults and prevents serious damage in the conveyor. Therefore, many fault detection algorithms were proposed to increase the safety and reliability of conveyor system [8-10]. Li, X. G. et al. [8] proposed the fault detection algorithm named Modified Regular Bands based on X-ray image to monitor the status of steel cord conveyor belt. Jiang, X. P. et al. [9] proposed a belt conveyor roller fault audio detection based on the wavelet neural network. Kanmani, M. [10] proposed faults such as belt tear up faults, oil level reduction fault, fire occurrence fault by using PLC and SCADA. However, this method had high computational cost. Therefore, to deal with these problems, this paper proposes an improved fault detection algorithm for the CS with known mathematical model and low computational cost. In this paper, a fault detection algorithm based on EKF is proposed. From the EKF, the estimated angular velocity indicates the encoder failure. The estimated friction indicates the mechanical failure Fault isolation is obtained by the friction bound. 2. SERVO CONTROLLER DESIGN The state dynamic equation of a given system with disturbance  can be expressed as follows: 1498
2. x Ax Bu  (1) y vL Cx 0 1 0 2 where ABCR , ,  b 0 , a1 bJL L ,,, a 2 RKJ b L b 1 RRKJ a b L a2 a 1 b 1 TT x  x12 x L  L ,, u  m v L R b  L where vL is the belt linear velocity, K is the spring constant of belt and  is related to load, tension, etc. It is assumed that (,)AB is controllable and (,)AC is observable. The output error is defined by e y y r (2) The servo control system design is attempted by 3 steps as follows: [Step 1] eliminate the effect of disturbance in Eq. (1) by operating the polynomial qq 1 differential operator of LDDD() q 10 L to both sides of Eqs. (1) and (2): d {()}()()LDx ALDx BLDu dt (3) L()() D e CL D x where D d/ dt , L( D ) yr 0 and LD( ) 0. [Step 2] an extended system is obtained by using the operated system through the step 1 as follows: xe A e x e B e (4) where L() D x 0 1 0L 0 e 0 0 1L 0 AB0 0 (1) MMMOM ABMee ,,, T xNe e , MN 0 c1 M 0 0 0L 1 (q 1) L e 0 1 2q 1 [Step 3] by defining a new control law, v , and a new error variable vector, z, as Eq. (5), the extended system of Eq. (4) can be written by Eq. (6) as follows: v L() D u Fxe 1 (5)  L() D z d x  A BF x BF  Ax Bu  dt xz (6) d  N I e dt T I 0 0L 1T , where 12 L  q ,    LD( ) 0, FFF  xz is a feedback control gain matrix, and the second term of Eq. (6) is a servo compensator for Eq. (1). The configuration of the proposed servo control system can be described as shown in Fig. 1. 1499
3. -  yr e  - u x y  Nz I e Fz x Ax Bu  C - + Fx Fig. 1 Proposed servo control system 3. FAULT DETECTION ALGORITHM 3.1 Extended Kalman Filter The EKF consists of two steps as follows [11]: Prediction step: xˆˆk| k 1 f (,) x k 1| k 1 u k 1 TT PFPFWQWk| k 1 k 1 k 1| k 1 k 1 k k 1 k f Fk 1 (7) x xuˆ k 1| k 1, k 1 f Wk u xuˆ , k 1| k 1 k 1 where xˆ kk|1 is the predicted state estimate at time k, and Pkk|1 is the predicted covariance matrix estimate at time k. Update step: yk z kh() xˆ k|1 k T SHPHRk k k|1 k k k T 1 KPHSk k|1 k k k xˆˆk| k x k | k 1 K k y k yk z kh() xˆ k|1 k (8) PIKHPk| k () k k k | k 1 h i Hik , xi xikk|1 where yk is the measurement innovation at time k, zk is the output vector from estimation at time k, h()xˆ kk|1 is the measurement result, Sk is the innovation covariance at time k, Rk is the measurement noise covariance at time k, K k is the Kalman gain at time k, xˆ kk| is the updated state estimation at time k, and Pkk| is the updated covariance matrix estimation at time k. 3.2 Fault detection and isolation using EKF From the EKF, the estimated angular velocity,  , and the estimated friction, b , can be obtained. The estimated angular velocity indicate the encoder failure. The estimated friction indicate the mechanical failure. The fault condition is as follow: 1500
4. normal 0 if  Th and b Th Fault condition 12 (9) fault 1 if  Th12 orb Th The threshold value Th1 and Th2 is predetermined and constant based on experiment data. 4. EXPERIMENTAL RESULTS 4.1 Experimental results of servo controller design Experimental results are shown in Figs. 2. The outputs of the PI controller have steady state errors in cases of ramp reference input. The outputs of MRAC controller can track the reference input more slowly than those of the proposed method. Only the outputs of the controller using the proposed method can track this type of reference input and the plant can be stabilized after finite time. Fig. 2 Control law u, output error e, output y for trapezoidal velocity profile yr 4.2 Experimental result of fault detection algorithm The experimental results for fault detection are shown in Fig. 3. Fig. 3(a) shows the experimental results for normal condition. Fig. 3(b) shows that the estimated friction values increased over the threshold value Th2 2 Nms at t = 5s. It indicate the mechanical fault. Fig. 3(c) shows that the estimated angular velocity increased over the threshold value Th1 300 rpm at t = 4s. It indicate the encoder fault. (a) (b) (c) Fig. 3 (a) Normal condition, (b) Mechanical fault detection, (c) Encoder fault detection 5. CONCLUSION This paper proposed a servo controller design and fault detection algorithm for CS. The experimental results of the servo controller design showed that the performance of the proposed method satisfied the requirement at a speed of 5.2 m/s. The experimental results of fault detection showed that the proposed algorithm successfully detected the mechanical fault conditions and encoder fault detection. The algorithm calculated the estimated based on EKF. In the future, this system can be improved so that it can detect more than one fault at a time. 1501
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