Model identification and control analysis for underwater thruster system

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1 Indian Journal of Geo-Marine Sciences Vol. 42(8), December 2013, pp Model identification and control analysis for underwater thruster system R. Mohd-Mokhtar 1, M.H.R.A. Aziz 2, M.R. Arshad 3, A.B. Husaini 4 & M.M. Noh 5 1,2,3,5 Underwater Control Robotics Research Group (UCRG), School of Electrical and Electronic Engineering Universiti Sains Malaysia, Engineering Campus Nibong Tebal, Pulau Pinang, Malaysia 4 Manufacturing Section, Universiti Kuala Lumpur Malaysian Spanish Institute (UniKL MSI) Lot 13-16, Kulim Hi-Tech Park, Kulim Kedah, Malaysia [ rosmiwati@ieee.org 1 ; mhilmiee87@gmail.com 2 ; rizal@eng.usm.my 3 ; muhamadhusaini@msi.unikl.edu.my 4 ; maziyah@ump.edu.my 5 ] Received 5 December 2012; revised 13 September 2013 This paper conducts an analysis to obtain underwater thruster model using system identification approach. Performance of the developed model is further analysed by simulating it with PID control system. Four realization approaches are investigated whereby methods that carry the highest best fit value are chosen. Open loop and closed-loop control analysis are run for this purpose. From results, model which have best fit value of 98% able to provide good performance for open loop deployment analysis, whereas models with accuracy around 70% only unable to give satisfactory result. However, all the models show good performance for closed-loop analysis, in which, the PID controller model has played a role in improving the system performance. [Keywords: Underwater vehicle, Thrusters system, System identification, PID control] Introduction Recently, the development of Autonomous Underwater Vehicle (AUV) has focusing on producing underwater thruster which is high performance, low cost and easy to integrate. Most of the advanced research directed towards the design in the outer loop control system, speed of Remotely Operated Vehicles (ROV), manoeuvring and positioning system for the AUV 1-4. Meanwhile, the design of thruster that involved of motor coupled propeller system has less attention. The focus and study on the thruster system with speed controller and output feedback of the estimated axial flow velocity become unfamiliar due to the difference in thruster performance while mounted on the body of the AUV. Thrusters modelling and control is one of the core elements that need to be considered for underwater vehicle control and simulation 5. Reference 6 proposed an accurate four quadrant nonlinear dynamical model for marine thruster, based on theory and experimental validation. This approach presents thruster model incorporate with the effect of rotational fluid velocity and inertia on thruster response and also the experimental approach to determine sinusoidal lift and drag curve. The model was succeeded but many questions remain unsolved as sinusoidal drag and lift curve models disagreed in experimental results. Thruster i s usually propellers which are driven by electrical motors. The thruster subsystem includes motor model, propeller model and hydrodynamics model. Motor block model responsible for converting electric power input to mechanical force. Propeller block model will be driven by motor to produce thrust and torque on the thruster. Hydrodynamics block model is a feedback from propeller to the motor input. To obtain a model for each of the subsystem, the modelling and control is usually employed using first principle modelling approach 7. However, in this paper, the system identification approach is used. System identification is known as empirical modelling approach, in which, model of the system is developed based on the input and output data collected from the system or plant 8. In general system identification procedures consist of four main steps 8 ; experimental design where the input and output data are recorded, model structure selection where appropriate model structure is chosen and its type, size and parameterization is determined based on the intended purpose, parameter estimation where the parameter is optimized to fit the observed data based on the selected criterion and model

2 MOKHTAR et al.: MODEL IDENTIFICATION AND CONTROL ANALYSIS FOR UNDERWATER THRUSTER SYSTEM 993 validation where the performance of the estimated model is verified. There are a few techniques that can be used to validate the estimated model such as 8 1 Validation with respect to the purpose of the modelling: For model that is required for the regulator design, prediction and simulation. 2 Validation over feasibility of the physical parameters: For model that is parameterized in terms of physical parameters. 3 Consistency and sensitivity validation: To show how well the dynamics have been captured. 4 Model reduction technique: To observe the complexity of the system. 5 Simulation and prediction test. For examples means squares error test, best fit test, k-step ahead prediction, cross-validation, variance accounted for test etc. 6 Residual analysis. In this study the purpose of having the underwater thruster model is to use it for control design simulation. Thus, with the assumption that a good model will provide a good control for model-based control analysis, this paper is aimed to evaluate how well the performance of the thruster model that is developed via system identification approach with acceptable accuracy (based on validation technique number 5) to perform during the deployment stage (validation technique number 1). Materials and Methods The flow chart showing the sequence of process that has been conducted in this study is given in Figure 1. The following subsections will explain the details. Figure 2 shows the underwater thruster design that was developed in the UCRG lab. This motor was designed to work at a maximum depth of 300 metres underwater. The motor is of a Brushless Permanent Magnet DC type. The overall weight of the motor was 25 Newton in air and 19 Newton underwater. This motor can exert a maximum of 48 volts and 15 amps of current. The entire thruster system consists of a few subsystems; those have certain function to make the thruster work properly. The thruster subsystem includes motor model, propeller model and hydrodynamics model (Figure 3). Motor model converts the electric power supply in terms of voltage and current to the mechanical force. For marine thruster model, brushless DC motor which powered by direct-current electricity (DC) has been used. Voltage and current supplied to the motor are controlled by a motor driver. Commutation system of this BLDC (Brushless DC) motor is controlled by electronic system of the motor driver. The motor will drive the shaft to rotate in desired output revolution speed. At the end of the motor shaft, the propeller is attached. Propeller produced Fig. 1 Flow of process

994 INDIAN J. MAR. SCI., VOL. 42, NO. 8 DECEMBER 2013 Fig. 2 CAD for an underwater motor Fig. 4 Data acquisition setup Fig.

Since the water is a load as induced by propeller, the motor load in term of propeller torque is feedback to the motor.

The torque hydrodynamic opposed the torque produced by motor, thus it becomes the loading torque for the motor itself. For underwater testing, a specific data logging circuit is developed.

After discretization, the data was sent to a PC by using a serial link. Following that, the data was read through a hyper terminal and then saved as a text file.

3 994 INDIAN J. MAR. SCI., VOL. 42, NO. 8 DECEMBER 2013 Fig. 2 CAD for an underwater motor Fig. 4 Data acquisition setup Fig. 3 Input output of thruster model thrust, torque and velocity that are related to drag and lift forces on the wing bladed propeller according to the lift and drag relationship. Since the water is a load as induced by propeller, the motor load in term of propeller torque is feedback to the motor. Propeller torque is also known as hydrodynamic torque, due to the influence of water hydrodynamic through propeller blades. The torque hydrodynamic opposed the torque produced by motor, thus it becomes the loading torque for the motor itself. For underwater testing, a specific data logging circuit is developed. This data acquisition circuit is developed using PIC 16F877A (Figure 4). The data from the load cell is sent to the data acquisition circuit for discretization. After discretization, the data was sent to a PC by using a serial link. Following that, the data was read through a hyper terminal and then saved as a text file. During this acquisition procedure, the water surrounding the propeller remained static and only the propeller rotational speed is changed. The power drained by the motor is assumed as power input to the propeller. Thus, by using current and voltage input to the thrusters motor, thrust reading is recorded on the computer. The input and output of raw data measured from the thrusters system is shown in Figure 5. Fig. 5 Plot of input and output data Model Identification In obtaining a transfer function model of thruster system, 4 different identification approaches are used: PEM Prediction Error Method N4SID State Space Subspace System Identification 2-Stage ID Two-stage identification Direct ID Direct Identification The PEM method comes from a family of prediction error optimization approach which was developed by Astrom, Bohlin and Eykoff PEM method determines the model parameters by minimizing the predicted error. PEM is the common method to be used in parameter estimation process. Details description for the algorithms can be referred in 11. N4SID comes from a state-space subspace realization approach introduced by Van Overschee and De Moor In this approach, the relationship between the input, noise and the output signals is written as a system of first-order differential or difference equations using an auxiliary state vector x(t). N4SID performs an oblique projection of future outputs along future inputs onto the past data.

4 MOKHTAR et al.: MODEL IDENTIFICATION AND CONTROL ANALYSIS FOR UNDERWATER THRUSTER SYSTEM 995 Then, SVD (Singular Value Decomposition) on the projection result will develop estimates of state variables. The system matrices are estimated by least square regression. In this paper, the N4SID method and the PEM method are run using the Matlab System ID Toolbox 14. For both, the identification procedure is run in discrete time domain. The remaining two approaches are identification algorithms that are developed using MOESP (Multivariable Output Error State Space) approach that was originally proposed by Verhaegen and Dewilde The 2-stage ID involves a frequency sampling filter (FSF) model at the first stage followed by the M O E S P approach on the second stage. Here, the first stage of identification using FSF approach will be used to eliminate the noise effects and also to provide with unbiased estimates. This tool is also able to outcome a so called compressed data. Raw data will be analyzed and only an important and meaningful parameter that describes the empirical model of the analyzed data will be captured. FSF approach involves the use of Finite Impulse Response (FIR) model and the maximum likelihood method which plays a role in eliminating the bias and noise effects of the data collected from closed-loop systems 17. Next, the Prediction Error Sum of Square (PRESS) technique is also employed. This tool will determine the precise value of the model and to ensure the final FSF model has the greatest predictive capability among all the prescribed candidates 18. The step response estimates obtained from the first stage will be next used on the second stage, in which, a continuous time subspace identification will be conducted in order to get the state-space model of a thruster system. Laguerre filter network will be utilized to the step output, y, and unit step input, u, before MOESP method conduct the identification process. By taking advantage of the orthonormal properties of the Laguerre functions, a continuous time state-space model with minimum error in a least square sense can be produced in the subspace identification process. References discussed the details descriptions about this method. On the other hand, the Direct ID approach adopting direct raw input output data with subspace identification procedure to obtain the model of the system. During this procedure, MOESP approach will be used directly in order to develop a model of the thruster. The different between Direct and 2-stage ID is on the involvement of FSF approach. MOESP method is based on the extended observability matrix for the system matrices. It performs a recursive quadratic (RQ) factorization of the input and output data. Then, the extended observability matrix is estimated from a part of the coefficient matrix by the singular value decomposition For both 2-stage ID and Direct ID, the identification procedure is run in continuous time domain. Overall, the similarity and differences of the approaches are dictated as follow. All the four approaches come from realization identification family. Except for 2-Stage ID, the other three approaches use direct identification of the input and output data. N4SID and PEM methods are running in discrete time domain using the MATLAB system identification toolbox, whereas the 2-Stage ID and Direct ID are running in continuous time domain via simulation of the algorithm using MATLAB code generation. PID Control System Once the model is obtained, the control simulation analysis is run based on PID control. A proportional integral derivative controller (PID controller) is a generic control loop feedback mechanism (controller) that is widely used in industrial control systems This is a type of feedback controller whose output, a control variable (CV), is generally based on the error (e) between some user-defined set point (SP) and some measured process variable (PV). The PID controller calculation (algorithm) involves three separate parameters, and is accordingly called three-term control: the proportional, the integral and derivative values, denoted K p, K i, and K d. Each element of the PID controller refers to a particular action taken on the error 26. Proportional: error multiplied by a gain, K p. This is an adjustable amplifier. In many systems K p is responsible for process stability: too low and the PV can drift away; too high and the PV can oscillate. Integral: the integral of error multiplied by a gain, K i. In many systems K i is responsible for driving error to zero, but to set K i too high is to invite oscillation or instability. Derivative: the rate of change of error multiplied by a gain, K d. In many systems K d is responsible for system response: too high and the PV will

5 996 INDIAN J. MAR. SCI., VOL. 42, NO. 8 DECEMBER 2013 oscillate; too low and the PV will respond sluggishly. The reason of choosing the PID control in this paper is due to the simplicity of the control implementation (since the aim is to observe the thruster model performance rather than the controller model) and the availability of technique for tuning the controller gain. Value of K p, K i and K d are determined as shown in Table 1. The open loop and closed-loop control analysis are conducted in order to see which model will give a good control performance. Results and Discussion During the conduct of system identification procedure, the best fit values according to the following equation are calculated. y ŷ BF = 1 100% y y (1) Where y Measured output ŷ Estimated output y Mean output This evaluation test is used as it is the tool that has been used in the Matlab System Identification toolbox to measure the fit between the measured and the estimated output. From calculation, the percentage of accuracy based on best fit is tabulated in Table 2. It shows that the 2-stage ID gives the best accuracy as compared to the other three methods. The N4SID, Direct ID (via MOESP) and PEM method give about the same performance accuracy. Higher accuracy is expected from the 2-Stage ID approach since the process of removing noise and retaining only the meaningful parameter that described the thrusters Table 1 PID Gain system is employed using the FSF model at the first stage of the identification. Thus, the MOESP method which has been employed within the second stage is able to model the system successfully. From the conducted identification processes, the following transfer function models of thruster system are obtained. 2-Stage ID: Direct ID: N4SID: PEM: The transfer function model obtained after this process is then used in simulation control of the thruster system. Figure 6 until Figure 9 show the results obtained from open loop and close d-loop response using PID control for each identification approach. K p K d K i N4SID PEM Stage ID Direct ID Table 2 Accuracy test results Identification Method Best Fit (%) N4SID 75 PEM 73 2-Stage ID 98 Direct ID 74 Fig. 6 Open loop and closed-loop N4SID response

6 MOKHTAR et al.: MODEL IDENTIFICATION AND CONTROL ANALYSIS FOR UNDERWATER THRUSTER SYSTEM 997 Fig. 7 Open loop and closed-loop PEM response Fig. 8 Open loop and closed-loop 2-Stage ID response From observation over an open loop response (Figures 6-9), the results are varies for all the models tested. It is seen that the 2-stage ID model provides significant meaning from the response. For the N4SID, it shows that the system takes longer time to reach the steady state, whereas oscillation occurred for PEM model. As for the Direct ID model, the response does not carry any significant meaning at all. From this analysis, it shows that only model with accuracy very close to 100% able to give significant performance. For the model having percentage below than 80%, the ability of the model to truly describe the system is not guaranteed. Fig. 9 Open loop and closed-loop Direct ID response Once the PID control loop is applied, the models are tuned and the PID control gain for each model is as shown in Table 1. Satisfactory performances are shown of all the output response from all the models (Refer to Figures 6-9). These results show that the PID controller model has played a role in tuning and improving the performance of the overall system. However, with respect to overall good performance (from identification to control), it can be concluded that the 2-stage ID has good domination of all. From these analyses, two issues are raised. Though the same data is used to develop the model, the accuracy of the developed model is subjected to the method that is used during the identification procedure. The open loop analysis is considered as a prior step before conducting the closed-loop control as the information in terms of stability and setting up the tracking references for further analysis can be done. However, it is truly depended on the accuracy of the developed plant model. Good model will give good starting information for next control system design. Conclusion Model identification and PID control analysis was run for thruster system. System identification approach based on 2-stage ID, Direct ID, N4SID and PEM methods were used to obtain the transfer function model of the system. Results show that the highest best fit value belongs to the 2-stage ID method. In control analysis, the model obtained from 2-stage ID also gives good performance over open

7 998 INDIAN J. MAR. SCI., VOL. 42, NO. 8 DECEMBER 2013 loop and closed-loop analysis. The outcome from this analysis has increased the confidence with respect to validation over model accuracy and ability to demonstrate good control performance. In this case the model developed from 2-Stage ID approach has proven the efficacy. Acknowledgments Authors would like to thank Universiti Sains Malaysia for the awarded short term grant to support this project. References 1 Krieg, M. and Mohseni, K. Dynamic Modeling and Control of Biologically Inspired Vortex Ring Thrusters for Underwater Robot Locomotion. IEEE Transactions On Robotic, 26(3): , Qing-ming, C., Fang-wen, H., Deng-hai, T., Fang-lin, H., and Lin-zhang, L. Prediction of Loading Distribution and Hydrodynamic Measurements for Propeller Blades in A Rim Driven Thruster. Journal of Hydrodynamics 24 (1): 50-57, Sarkar, T., Sayer, P. G. and Fraser, S. M. A Study of Autonomous Underwater Vehicle Hull Forms Using Computational Fluid Dynamics. International Journal for Numerical Methods in Fluid, 25: , Qiuling, J. and Li, G. Formation Control and Obstacle Avoidance Algorithm of Multiple Autonomous Underwater Vehicles (AUVs) Based on Potential Function and Behavior Rules. IEEE International Conference on Automation and Logistics, Kim, J. Thruster Modelling and Controller Design for Unmanned Underwater Vehicles (UUVs). Austria: In-Tech, Bachmayer, R. and Whitcomb, L. L. An Accurate Four- Quadrant Nonlinear Dynamical Model for Marine Thrusters: Theory and Experimental Validation. IEEE Journal of Oceanic Engineering, 25(1): , Yoerger, D. R., Cooke, J. G. and Slotine, J. E. The Influence of Thruster Dynamics on Underwater Vehicle Behavior and Their Incorporation into Control System Design. IEEE Journal of Oceanic Engineering, 15(3): , Astrom, K.J. Maximum likelihood and prediction error methods. Automatica, 16: , Bohlin, T. On the problem of ambiguities in maximum likelihood identification, Automatica, 7: , Eykoff, P. Some fundamental aspects of process-parameter estimation, IEEE Trans. on Automatic Control, 8: , Ljung, L. 2 nd eds System Identification: Theory for the User. New Jersey: Prentice. 12 Van-Overschee, P. and De-Moor, B. N4SID: Numerical algorithms for state space subspace system identification, 12 th IFAC World Congress, pp , Sydney, Australia, Van-Overschee, P. and De-Moor, B. N4SID: Subspace algorithms for the identification of combined deterministicstochastic systems, Automatica, 30(1):75-93, Ljung, L. System Identification Toolbox: For Use with MATLAB. USA: The MathWorks Inc, Verhaegen M. and Dewilde, P. Subspace model identification Part I: The output error state-space model identification class of algorithm, Int. J. Control, 58: , Verhaegen M. and Dewilde, P. Subspace model identification Part II: Analysis of the elementary output error state-space model identification algorithm, Int. J. Control, 56(5): , Wang, L. and Cluett, W. R. Frequency sampling filters: An improved model structure for step-response identification. Automatica, 33(5): , Wang, L. and Cluett, W. R. Use of PRESS Residuals in Dynamic System Identification. Automatica, 32: , Mohd-Mokhtar, R. and Wang, L. 2-stage approach for continuous time identification using step response estimates. IEEE Int. Conf. on Systems, Man & Cybernetics, Singapore, Aziz, M. H. R. A. and Mohd-Mokhtar, R. Identification of MIMO Magnetic Bearing System Using Continuous Subspace Method with Frequency Sampling Filters Approach. 37th Annual Conference of the IEEE Industrial Electronics Society, Melbourne, Australia, Aziz, M. H. R. A. and Mohd-Mokhtar, R. Model Identification for Underwater Glider System Using Two Stage Identification Approach. ASEAN Symposium on Automatic Control, Ho Chi Minh City, Vietnam, Katayama, T. Subspace Methods for System Identification. Kyoto, Japan: Springer, Mohd-Mokhtar, R. Continuous Time State-space Model Identification with Application to Magnetic Bearing Systems. Ph.D. diss. RMIT University, Melbourne, Australia, Dorf, R.C. and Bishop, R.H. Modern control systems, New Jersey: Pearson Education Inc., Astrom, K.J. and Wittenmark, B. Adaptive control, Reading: Addison-Wesley, Astrom, K.J. Control system design, Lecture Notes, University of California, 2002.

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