Parameter Estimation Technique of Nonlinear Prosthetic Hand System

This paper illustrated the parameter estimation technique of motorized prosthetic hand system. Prosthetic hands have become importance device to help amputee to gain a normal functional hand. By integrating various types of actuators such as DC motor, hydraulic and pneumatic as well as mechanical part, a highly useful and functional prosthetic device can be produced. One of the first steps to develop a prosthetic device is to design a control system. Mathematical modeling is derived to ease the control design process later on. This paper explained the parameter estimation technique of a nonlinear dynamic modeling of the system using Lagrangian equation. The model of the system is derived by considering the energies of the finger when it is actuated by the DC motor. The parameter estimation technique is implemented using Simulink Design Optimization toolbox in MATLAB. All the parameters are optimized until it achieves a satisfactory output response. The results show that the output response of the system with parameter estimation value produces a better response compare to the default value KeywordParameter estimation, Prosthetic hand, Lagrangian equation, Dynamic modeling


II. METHODOLOGY A. Simulation Model of Linear and Nonlinear Prosthetic Finger Movement System
This part describes the result from the Euler Lagrange that need to be simulate in order to see the data response. By using Simulink in MATLAB software the equation from Euler Lagrange can be identify to be usable or not. Fig. 1 shows the subsystem in block diagram of the Prosthetic Finger System. This part describes the result from the Euler Lagrange that need to be simulate in order to see the data response. By using Simulink in MATLAB software the equation from Euler Lagrange can be identify to be usable or not. Fig. 1 shows the subsystem in block diagram of the Prosthetic Finger System.  Fig. 6 [3]. The control parameter of the system is a position/ theta. The specifications of payload which will be used in finger movement system are described in Fig. 3. From the figure of subsystem, it shows that the voltage as the input and position/theta as the output. All the parameter has been tabulated in Table 1 and is set as in Fig. 4.
Step input is applied as an input voltage and it has been set as 1 Volts. The step input signal is representing as the supply to operate movement of finger.
Step input is the time behavior of the output of a general system when its input changes from zero to one in a very short time. The performance of finger movement system is analyzed.   ) is the method to estimate and optimize the output of plant system approximate with the real data output response as shown in Fig. 5. The non-linear plant system is preferable because the linear plant system will eliminate some variable from the original equation In order to estimate any real value of plant system, datasheet motor is important instead of mathematical formula to find the default value [4]. As an example, in this experiment is to find torque constant (Kt), torque electric(Ke), gear ratio(z) and resistance(R) by using this method. Parameter estimation is a method to get the limit/range of parameter that no declare by the manufacturer. At the end of this method, after several iteration as shown in Fig. 6, the output response of the plant based on the parameter estimation value is compared with the real data output response to check the validity of the value  In some cases, linearization of a nonlinear system is normally obtainable by using Jacobian matrix equilibrium point. Then, by using the linearized system, a simple linear controller can be applied to achieve stabilization. However, the controller will not be able to guarantee stabilization beyond the wide range of non-linear sector. The contradiction between the actual non-linear system and its linearized version would devise a cunning test to control engineers. In fact, stabilizing task becomes difficult when non-linearity is to taken into consideration and linearization model of such system is omitted. The contradiction between the actual non-linear system and its linearized version in Fig. 7 would devise a cunning test to control engineers. The difference between linear and non-linear output responses caused by the certain parameter that have been eliminated during the linearization such as sin theta will be cancelled out from the equation because the value is too small and cos theta will be turned to one because the linearization condition.

B. Estimation Parameter Nonlinear Plant System
In this research, the output of a nonlinear response of plant system is position / theta. Only real output position data response was taken to compare with the non-linear parameter and optimized the unknown value parameter. Fig. 8 shows the real data form the system identification process that is fed into the Simulink design optimization toolbox. The unknown parameter value such as Torque Constant (Kt), Torque Electric (Ke), Gear ratio (z), and Resistance(R) were the unknown parameter in the non-linear plant system. By using optimization parameter, each of the values can be automatically discovered. Fig. 9 shows the trajectories of estimating parameters process from the measured data (non-linear plant system) approximate with real output response data. Figure 10 shows the measured and simulated output response of the system.  Fig. 11 shows the position output response before optimization using estimation parameter and Fig. 12 shows the output response after optimization. The result after the optimized process shows similar output position approximate with the real data position output response.

C. Euler Lagrange Nonlinear Plant System with PID
The P, I and D terms need to be "tuned" to suit the dynamics of the process being controlled. Any of the terms described above can cause the process to be unstable, or very slow to control, if not correctly set. These days temperature control using digital PID controllers have automatic auto-tune functions. During the auto-tune period the PID controller controls the power to the process and measures the rate of change, overshoot and response time of the plant [5]. Fig. 13 shows the PID controller performance with the optimized parameter estimation values. It shows acceptable response compare to the previous paramater values.  Based on Table 2, it is not arguable that the after tuned performance has an acceptable performance to be implemented in this prosthetic hand research analysis. It offers fastest rise time (Tr), settling time (Ts), however, the percentage of overshoot is higher than the output response before tuned (block). Thus, the tuned PID Controller is preferable than block output response and this tuned output response have been decided to use as PID controller for this particular analysis [6] Fig. 14 shown both of two systems with PID and without PID controller output response respectively. We can conclude that the with PID controller output response manage to meet the requirement stage during the design stage. By referring figure above, the rise time of without PID system performance dramatically increased compared with the with PID system. The increment then caused the output response of without PID system was not stable. Thus, PID controller manages to produce a good performance result and stabilized the prosthetic finger system.

IV. CONCLUSION AND RECOMMENDATION
In conclusion, the unknown parameter value in this system can be estimated under certain condition which are the datasheet parameter and real data are required. It is because certain parameter not listed from the manufacturer. The analysis shows that the parameter estimation value produces a quite acceptable output response compare to the default value. Therefore, if any models that do not have complete parameter value in their manufacturer datasheet, parameter estimation technique can be performed.