Speed control for PMSM servo system using predictive functional control and extended

state observer

Department of Electrical EngineeringSouthern Taiwan University of Science and Technology

Huixian Liu and Shihua Li, Senior Member, IEEE

IEEE TRANSACTION ON INDUSTRIAL ELECTRONICS, VOL. 90, NO. 2, FEBRUARY 2012

Teacher : Prof. Ming-Syhan Wang

Student : Nana SutarnaID Student: DA230208

Out lineAbstractI. IntroductionII. Preliminaries

A. Mathematical Model of PMSMB. Outline features of Predictive Functional Control method 1. Base functions 2. prediction Model 3. Error Correction 4. reference Trajectory 5. Receding Optimization

III. Design of Speed Controller A. Simple Model of PMSM B. Design Based on PFC

1. Base functions 2. prediction Model 3. Error Correction 4. reference Trajectory 5. Cost Function

C. Simulation and Experimental Result (PFC) D. Design Based on PFC and ESO E. simulation and Experimental Results (PFC + ESO)IV. Conclusion

Abstract1. To optimize the performance of PMS, Introducing Predictive Functional Control (PFC)

method2. The model is simplified to predict the future q-axis current 3. Optimal Control law is obtained by minimizing a quadratic performance index.4. PFC + ESO is developed to estimate the lumped disturbances and also add forward

compensation 5. Simulation and experiment comparisons are made for PFC and PI method with

antiwindup control method

I. IntroductionDue to the existence of nonlinearities, uncertainties, and disturbances, conventional

linear control like PI can not guarantee a sufficiently high performance for PMSM servo system [2], [3]. In recent year many nonlinear control methods has been developed for the PMSM system such as linearization control [4], adaptive control [5], [6], robust control [7], [8], sliding mode control [9], [10], disturbance observer-based control [6], [11]-[13], [34], finite time control [12], fractional order control [14], fuzzy control [2], [15], neural network control [3],[15]. These approaches improve the control performance of the motor from different aspects.

Model Prediction Control (MPC) is one of the most practical control technique can be regarded as a kind of optimal control method, which employs a dynamic model of plant to forecast the future behavior of states and determines the future control action according to optimization of a certain performance target function or an operating cost function at each sampling time [17], [18].

The advantages of MPC method can ensure a satisfying system performance such as robustness, simplicity of modeling, and good capability of handling constraints of both manipulated and controlled variables.

The disadvantage of MPC method is need a cumbersome computation load at each sampling time.

• The main purpose this paper are:1. Simplified MPC method to became PFC2. The differential usage of MPC as PFC method to the control design of

speed loop.3. To improve PFC control method for the disturbance rejection ability of

the PMSM system.

• In this paper, to improve the disturbance rejection performance of the PFC control method is introduced a feedforward compensation part or Extended State Observer (ESO). It is called PFC+ESO method.

II. PreliminariesThe mathematical model of PMSM and outline of PFC methodA. Mathematical model of PMSM

B. Outline and features of PFC MethodPFC is a type of MPC method which can significantly reduce the volume of online computing and make it possible and also more suitable to be used in practical control of rapid dynamical system. The main idea can be summarized by the following points.

2. Prediction Model: This is the internal model which used for online prediction of the future output over a defined finite horizon. the prediction of the plant output is given in discrete model form

1. Base functions: Base function is a linear combination of functions which structured for the future manipulated variables

3. Error Correction: it is the error value between forecasted model output and practical output

4. Reference Trajectory : Reference trajectory is a reference model which provides a reference trajectory toward the desired trajectory or set point within a certain future time horizon. the main goal of this algorithm is to find a control law that enables the controlled signal to track the reference trajectory.

5. Receding Optimization: This is the optimal index as a future control value which achieved from tracking error between the predicted output and reference trajectory in prediction horizon.

II. Design Speed ControllerThis section introduces the main design steps of the PFCmethod for the speed loop of PMSMA. Simplified Model of PFCMPC controller can be easily implemented directly with understandable model,but for dynamic model like PMSM whose nonlinear and state coupled containSpeed ω with current id or iq, the linear model is required. Since the dynamics of current loopis usually much faster than that of speed loop, it can be assumed to be ignored, which impliesthat the current iq equals to the command currenti q,i.e.,Gi(s)≈1. Thus, the diagram of PMSM∗can be reduced to the diagram shown in Fig. 3.

B. Design Based on Predictive Function Control1). Base Functions:

Now, a new mechanical dynamic can be given in Laplace domain as a first-order model

2). Predictive Model: As previously mentioned, PFC design requires a discrete time model. Here, a discrete time mode, which is obtained by forward Euler discretization of (7).

3). Error Correction:

4). Reference trajectory:

5). Cost Function:

Therefore, the block diagram of the PMSM system using PFC method is shown in Fig. 4.

1) Simulation Result:

Parameter PI; Kp = 0.11, Ki = 30

Parameter PMSMRate Power (P) = 750 W ; Rated Voltage (U) = 200 V; Rated Current (IN) = 4.71 A;

Number of Pole (np) = 4; Armature Resistance (Rs) = 1.74 Ω; Stator inductances

(Ld =Lq = L) = 0.004 H; Viscous Damping (B) = 7.403 x 10-5 N.m.s/rad; Moment of inertia (J) = 1.74 x 10-4 Kg.m2 ; Rated speed (N) = 3000 rpm; Rotor flux = = 0.1167 wb; Rated Torque (TN) = 2.0 N.m.

Parameter PFC: sampling time (Ts) = 250 µs; The desire response time (Tr) = 50 µs;P = 6; Q = I6 x 6 ; r = 2 αm= 0.999.

C. Simulation and Experimental Result (PFC)

Fig. 5 and 6 show that PFC-based controller gives ashorter settling time with a smaller Overshoot compared with the PI control method in case 2000 rpm. Also when a load Torque TL= 2 Nm at applied at t= 0.5 s and removed at t=0.6 s, the standar PFC method has less speed fluctuations.

2. Experiment Result

The experimental setup for PMSM has done to evaluate the performance of the proposed method. The configuration of experimental test setup is shown Fig.7 and 8.

The control gain for both current loop are Kp = 42 and Ki= 2600, and for speed-speedControl, PI controller; Kp = 0.02, Ki = 29; PFC, Tr = 50 µs, P = 7, and Q = I7x7, r = 3.8, αm = 0.998.

The results are shown in Fig 9 and 10. the motor speed is 2000 rpm to reference speed. When steady state of 2000 rpm, TL = 2 .5 Nm is added and removed suddenly, It can be observed that PFC method shows a better disturbance rejection ability, with less speed fluctuations and shorter recovering times agains disturbances than PI.

D. Design Based on PFC and ESO

In order to improve the disturbance rejection performance of the PFC control method, a feedforward compensation is added. It is shown in Fig. 11.

Output of the system is measured speed ω, and motor dynamic equation from (1) can be written as:

The control input of compensate controller is

E. Simulation and Experimental Results (PFC + ESO)

1. Simulation Result

Parameter for PI + ESO speed are: -p = -4000, b0 = 5414, Ts = 50µs, P = 3, Q = I3x3, r= 1.8Αm = 0.999.

Fig.12 shows that compared with the PI and PIC method, the PFC + ESO method has the shortest settling time and smallest overshoot. It can be seen that, when a load torqueTL =2 Nm is applied at t = 0.5s and removed at t = 0.6s, the PFC + ESO-based controller hasa shortest recovering time and smallest fluctuations.

2. Experimental Result

Fig.13 shows the motor speed quickly converges to the reference shortly after starup when the reference speed is given as 2000 rpm. Compared with other two controller, PFC + ESO method shows a smallest overshoot and a shortest settling time.

Parameter for PI + ESO speed are: -p = -200, b0 = 1274, Ts = 50µs, P = 5, Q = I5x5, r= 2.8Αm = 0.9995.

The performance under sudden load disturbance impact, PFC + ESO-based controller hasa good disturbance rejection property while maintaining a good dynamic performance.

Considering the robustness of PMSM servo system, the comparison experiment result areShown in Fig. 14 – 17 when the reference speed signals are given as 1000 rpm and 500 rpm.

Considering the robustness of PMSM servo system, the comparison experiment result areShown in Fig. 14 – 17 when the reference speed signals are given as 1000 rpm and 500 rpm.

A comparison of performance indices on the three methods are shown in Tabel ! – III.

Conclusion1. The closed-loop system under PFC method has achieved a satisfying dynamic performance. 2. Incorporation PFC and ESO have improved the disturbance rejection ability of closed-loop. 3. The servo system under the composite PFC method can obtain a satisfying performance with fast transient response, good disturbances rejection ability.