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A New Approach of the Online Tuning Gain Scheduling Nonlinear PID Controller Using Neural Network

This chapter presents the design, development and implementation of a novel proposed online-tuning Gain Scheduling Dynamic Neural PID (DNN-PID) Controller using neural network suitable for real-time manipulator control applications. The unique feature of the novel DNN-PID controller is that it has highly simple and dynamic self-organizing structure, fast online-tuning speed, good generalization and flexibility in online-updating. The proposed adaptive algorithm focuses on fast and efficiently optimizing Gain Scheduling and PID weighting parameters of Neural MLPNN model used in DNN-PID controller. This approach is employed to implement the DNN-PID controller with a view of controlling the joint angle position of the highly nonlinear pneumatic artificial muscle (PAM) manipulator in real-time through Real-Time Windows Target run in MATLAB SIMULINK® environment. The performance of this novel proposed controller was found to be outperforming in comparison with conventional PID controller. These results can be applied to control other highly nonlinear SISO and MIMO systems.


Introduction
The compliant manipulator was used to replace monotonous and dangerous tasks, which has enhanced lots of researchers to develop more and more intelligent controllers for human-friendly industrial manipulators. Due to uncertainties, it is difficult to obtain a precise mathematical model for robot manipulators. Hence conventional control methodologies find it difficult or impossible to handle un-modeled dynamics of a robot manipulator. Furthermore, most of conventional control methods, for example PID controllers, are based on mathematical and statistical procedures for modeling the system and estimation of optimal controller parameters. In practice, such manipulator is often highly non-linear and a mathematical model may be difficult to derive. Thus, as to accommodate system uncertainties and variations, learning methods and adaptive intelligent techniques must be incorporated. Due to their highly nonlinear nature and time-varying parameters, PAM robot arms present a challenging nonlinear model problem. Approaches to PAM control have included PID control, adaptive control (Lilly, 2003), nonlinear optimal predictive control (Reynolds et al., 2003), variable structure control (Repperger et al., 1998;Medrano-Cerda et al.,1995), gain scheduling (Repperger et al.,1999), and various soft computing approaches including neural network Kohonen training algorithm control (Hesselroth et al.,1994), neural network + nonlinear PID controller (Ahn and Thanh, 2005), and neuro-fuzzy/genetic control (Chan et al., 2003;Lilly et al., 2003). Balasubramanian et al., (2003a) applied the fuzzy model to identify the dynamic characteristics of PAM and later applied the nonlinear fuzzy model to model and to control of the PAM system. Lilly (2003) presented a direct continuous-time adaptive control technique and applied it to control joint angle in a single-joint arm. Tsagarakis et al. (2000) developed an improved model for PAM. Hesselroth et al. (1994) presented a neural network that controlled a five-link robot using back propagation to learn the correct control over a period of time. Repperger et al. (1999) applied a gain scheduling model-based controller to a single vertically hanging PAM. Chan et al., (2003) and Lilly et al., (2003) introduced a fuzzy P+ID controller and an evolutionary fuzzy controller, respectively, for the PAM system. The novel feature is a new method of identifying fuzzy models from experimental data using evolutionary techniques. Unfortunately, these fuzzy models are clumsy and have only been tested in simulation studies. (Ahn and Anh, 2006) applied a modified genetic algorithm (MGA) for optimizing the parameters of a linear ARX model of the PAM manipulator which can be modified online with an adaptive self-tuning control algorithm, and then (Ahn and Anh, 2007b) successfully applied recurrent neural networks (RNN) for optimizing the parameters of neural NARX model of the PAM robot arm. Recently, we (Ahn and Anh, 2009) successfully applied the modified genetic algorithm (MGA) for optimizing the parameters of the NARX fuzzy model of the PAM robot arm. Although these control systems were partially successful in obtaining smooth actuator motion in response to input signals, the manipulator must be controlled slowly in order to get stable and accurate position control. Furthermore the external inertia load was also assumed to be constant or slowly varying. It is because PAM manipulators are multivariable non-linear coupled systems and frequently subjected to structured and/or unstructured uncertainties even in a well-structured setting for industrial use or human-friendly applications as well. To overcome these drawbacks, the proposed online tuning DNN-PID algorithm in this chapter is a newly developed algorithm that has the following good features such as highly simple and dynamic self-organizing structure, fast learning speed, good generalization and flexibility in learning. The proposed online tuning DNN-PID controller is employed to compensate for environmental variations such as payload mass and time-varying parameters during the operation process. By virtue of on-line training by back propagation (BP) learning algorithm and then auto-tuned gain scheduling K and PID weighting values Kp, K i and K d , it learns well the nonlinear robot arm dynamics and simultaneously makes control decisions to both of joints of the robot arm. In effect, it offers an exciting on-line estimation scheme.

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This chapter composes of the section 1 for introducing related works in PAM robot arm control. The section 2 presents procedure of design an online tuning gain scheduling DNN-PID controller for the 2-axes PAM robot arm. The section 3 presents and analyses experiment studies and results. Finally, the conclusion belongs to the section 4.

Experimental apparatus
The PAM manipulator used in this paper is a two-axis, closed-loop activated with 2 antagonistic PAM pairs which are pneumatic driven controlled through 2 proportional valves. Each of the 2-axes provides a different motion and contributes to 1 degree of freedom of the PAM manipulator (Fig. 1). In this paper, the 1 st joint of the PAM manipulator is fixed and proposed online tuning Gain Scheduling neural DNN-PID control algorithm is applied to control the joint angle position of the 2 nd joint of the PAM manipulator. A general configuration of the investigated 2-axes PAM manipulator shown through the schematic diagram of the 2-axes PAM robot arm and the experimental apparatus presented in Fig.1 and Fig.2, respectively. The experiment system is illustrated in Fig.2. The air pressure proportional valve manufactured by FESTO Corporation is used. The angle encoder sensor is used to measure the output angle of the joint. The entire system is a closed loop system through computer. First, initial control voltage value u 0 (t)=5 [V] is sent to proportional valve as to inflate the artificial muscles with air pressure at P 0 (initial pressure) to render the joint initial status. Second, by changing the control output u(t) from the D/A converter, we could set the air pressures of the two artificial muscles at (P 0 + P) and (P 0 -P), respectively. As a result, the joint is forced to rotate for a certain angle. Then we can measure the joint angle rotation through the rotary encoder and the counter board and send it back to PC to have a closed loop control system.  The experimental apparatus is shown in Fig.3. The hardware includes an IBM compatible PC (Pentium 1.7 GHz) which sends the control voltage signal u(t) to control the proportional valve (FESTO, MPYE-5-1/8HF-710B), through a D/A board (ADVANTECH, PCI 1720 card) which change digital signal from PC to analog voltage u(t). The rotating torque is generated by the pneumatic pressure difference supplied from air-compressor between the antagonistic artificial muscles. Consequently, the 2 nd joint of PAM manipulator will be rotated. and all control software is coded in MATLAB-SIMULINK with C-mex S-function. Table 1 presents the configuration of the hardware set-up installed from Fig.2 and Fig.3 as to control of the 2 nd joint of the PAM manipulator using the novel proposed online tuning Gain Scheduling DNN-PID control algorithm.

Controller design
The structure of the newly proposed online tuning Gain Scheduling DNN-PID control algorithm using neural network is shown in Fig. 4. This control algorithm is a new one and has the characteristics such as simple structure and little computation time, compared with the previous neural network controller using auto-tuning method (Ahn K.K., Thanh T.D.C., 2005). This system with the set point filter and controller using neural network can solve the problems, which were mentioned in the introduction and is also useful for the PAM manipulator with nonlinearity properties.
The block diagram of proposed online tuning Gain Scheduling DNN-PID control based on Multi-Layer Feed-Forward Neural Network (MLFNN) composed of three layers is shown in Figure 5. In this figure, K, K p , K i and K d , are scheduling, proportional, integral and derivative gain while e p , e i and e d are system error between desired set-point output and output of joint of the PAM manipulator, integral of the system error and the difference of the system error, respectively. MLFNN network is trained online by the fast learning back propagation (FLBP) algorithm as to minimize the system error between desired set-point output and output of joint of the PAM manipulator.
www.intechopen.com From Figure 5, the input signal of the Hyperbolic Tangent function f(.) becomes and y(k) are the desired set-point output and output of joint of the PAM manipulator. Furthermore, B i , K p , K i and K d are weighting values of Input layer and B h and K are weighting values of Hidden layer. These weighting values will be tuned online by fast learning back propagation (FLBP) algorithm. As to online tuning the gain scheduling K and PID parameters K p , K i and K d , the gradient descent method used in FLBP learning algorithm using the following equations were applied.
and the Bias weighting values B i (k) and B h (k) are updated as follows: where η, η p , η i , η d , η Bi and η Bh are learning rate values determining the convergence speed of updated weighting values; E(k) is the error defined by the gradient descent method as follows Apply the chain rule with equation 5 and 6, it leads to From equations 1, 3 and 6, the following equations can be derived A New Approach of the Online Tuning Gain Scheduling Nonlinear PID Controller Using Neural Network 9 From equations 8, 9 and 10, the following resulting equations can be derived From equation 5 and 6, the final equations for online tuning gain scheduling K and PID parameters K p , K i and K d are expressed as follows: www.intechopen.com and the Bias weighting values B i (k) and B h (k) are updated as follows:

Experimental Results
The performance of proposed online tuning gain scheduling DNN-PID control scheme is verified on joint angle position control of the 2 nd joint of the 2-axes PAM robot arm. Fig.3 and Fig.4 describes the working diagram of this control scheme. Fig.6 presents the experiment SIMULINK diagram of proposed online tuning DNN-PID control algorithm run in Real-time Windows Target with DYNAMIC_NEURAL_PID being subsystems written in C then compiled and run in real-time C-mex file. Three initial PID parameters K P , K I , K D and gain scheduling G value are chosen by trial and error method and determined as G=0.8; K P =0.09; K I =0.089 and K D =0.07.  The experiment SIMULINK diagram of the 2 nd joint of the 2-axes PAM robot arm position control using conventional PID controller in order to compare as to demonstrate the superiority of proposed control system. Three PID parameters K P , K I , K D and gain scheduling K value of conventional PID controller are chosen by trial and error method.
www.intechopen.com  (1) or the hyperbolic tangent function (0); the 6 th parameter contains logic value as to choose the linear function (0) or the sigmoid/hyperbolic tangent function (1) of Output layer; and the 7 th vector parameter contains the initial K, K P , K I , K D weighting values and two initial bias weighting values B i and B h . The final purpose of the PAM manipulator is to be used as an elbow and wrist rehabilitation robot device. Thus, the experiments were carried out with respect to 3 different waveforms as reference input (Triangular, Trapezoidal and Sinusoidal reference) with 2 different endpoint Payloads (Load 0.5[kg] and Load 2[kg]) as to demonstrate the performance of novel proposed online tuning DNN-PID controller. Furthermore, the comparisons of control performance between the conventional PID and two different methods of the proposed online tuning DNN-PID controller were performed. These two novel proposed methods compose of proposed online tuning DNN-PID-SIG and proposed online tuning DNN-PID-HYP. The 1 st method possesses the activation function of hidden layer of DYNAMIC_NEURAL_PID subsystem being Sigmoid function and the 2 nd method corresponds to the Hyperbolic Tangent function respectively. The initial gain scheduling value G and PID controller parameters K p , K i and K d were set to be G = 0.8, Kp = 0.089, Ki = 0.09, Kd = 0.07. These parameters of PID controller were obtained by trial-and-error through experiment. Forwardly, the two initial bias weighting values B i and B h are chosen equal 0.
First, the experiments were carried out to verify the effectiveness of the proposed online tuning DNN-PID controller using neural network with triangular reference input.  Figure   8a shows that PID controller caused the PAM manipulator response being oscillatory and unstable. Otherwise, proposed online tuning DNN-PID controller continues to assert robust control to keep PAM manipulator response stable and accurate tracking. In comparison between proposed DNN-PID-SIG and DNN-PID-HYP, both of proposed control algorithms obtain the excellent robustness and accuracy as well and thus are considered the performance equivalent. However in initial stage, proposed DNN-PID-SIG possesses significant overshoot which may cause unstable to PAM manipulator in its initial operation.        Figure 10a shows that PID controller caused the PAM manipulator response oscillatory and unstable. Otherwise, proposed online tuning DNN-PID controller continues to keep robust control as to maintain PAM manipulator response stable and accurate tracking.
In comparison between proposed DNN-PID-SIG and DNN-PID-HYP, proposed DNN-PID-HYP obtains the excellent robustness and accuracy in comparison with proposed DNN-PID-SIG and thus the proposed DNN-PID-HYP controller is considered to possess the best performance. Furthermore, in initial stage, proposed DNN-PID-SIG possesses again significant overshoot which may cause unstable to PAM manipulator in its initial operation. Figure 10c depicts the refined control voltage U applied to the joint of PAM manipulator, which is generated by the proposed online tuning DNN-PID controller as to assure the performance and the accuracy of the PAM manipulator response.    In comparison between proposed DNN-PID-SIG and DNN-PID-HYP, in this case of critical sinusoidal reference input 0.2[Hz], proposed DNN-PID-HYP once more obtains the excellent robustness and accuracy in comparison with proposed DNN-PID-SIG and thus the proposed DNN-PID-HYP controller is considered to possess the best performance between them. Furthermore, in initial stage, proposed DNN-PID-SIG possesses again significant overshoot which may cause unstable to PAM manipulator in its initial operation.
www.intechopen.com In summary, novel DNN-PID controller using neural network was investigated in this paper. It has shown that the proposed method had a good control performance for the highly nonlinear system, such as the PAM manipulator. The controller had an adaptive control capability and the control parameters were optimized via the back propagation algorithm. The controller designed by this method does not need any training procedure in advance, but it uses only the input and output of the plant for the adaptation of proposed control parameters and can tune these parameters online iteratively. From the experiments of the position control of the PAM manipulator, it was verified that the proposed control algorithm presented in this paper was online control with simple structure and had better dynamic property, strong robustness and it was suitable for the control of various plants, including linear and nonlinear process, compared to the conventional PID controller. In comparison between 2 proposed DNN-PID-SIG and DNN-PID-HYP control algorithms, based on experiment results, proposed DNN-PID-HYP control obtains the excellent robustness and accuracy in comparison with proposed DNN-PID-SIG and thus the proposed DNN-PID-HYP controller is considered to possess the better performance than the proposed DNN-PID-SIG one.

Conclusions
An innovative online tuning gain scheduling neural DNN-PID Controller suitable for realtime human-friendly industrial applications has been designed, developed and implemented for position control the joint angle of the experimental PAM manipulator in this paper. Experiment results show that the proposed online tuning Gain Scheduling DNN-PID controller is able to learn the nonlinear and dynamic characteristics of the PAM manipulator quickly and thus reduce the tracking error to nearly zero in its operation. The performance of the online tuning gain scheduling DNN-PID controller was found to be very good and robust in the presence of external disturbances. Furthermore, with this proposed online tuning DNN-PID control algorithm, gain scheduling value G and PID parameters K p , K i and K d can be modified in real time and actual trajectories can be monitored as well. This facilitates testing under different input conditions and ensures future applications of the PAM manipulator as a rehabilitation device for stroke patients. It determines confidently that the proposed online tuning Gain Scheduling DNN-PID controller not only proves its superb performance in control the highly nonlinear PAM manipulator but also would be very efficient in control of other real-time industrial and human-friendly applications.