Home > On Replacing PID Controller with Deep Learning Controller for DC Motor System

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Kangbeom Cheon, Jaehoon Kim, Moussa Hamadache, and Dongik Lee

School of Electronics Engineering, Kyungpook National University, Daegu, Korea Email: ckb0120@naver.com, destiny-be@hanmail.net, assuom25@yahoo.fr, dilee@knu.ac.kr

I. INTRODUCTION The machine learning algorithms can lead to significant advances in automatic control. The biggest single advance occurred nearly four decades ago with the introduction of the Expectation-Maximization (EM) algorithm for training Hidden Markov Models (HMMs) [1]. With the EM algorithm, it became possible to develop control systems for real world tasks using the richness of Gaussian mixture models (GMM) [2] to represent the relationship between HMM states and the reference input. GMMs have a number of advantages that make them suitable for modeling the probability distributions over vectors of input features that are associated with each state of an HMM [3]. Despite all their advantages, GMMs have a serious short coming – they are statistically inefficient for modeling data that lie on or near a non- linear manifold in the data space [3]. Artificial neural networks trained by back-propagating error derivatives have the potential to learn much better models of data that lie on or near a nonlinear manifold [3]. Over the last few years, advances in both machine

Manuscript received September 11, 2014; revised December 21, 2014.

learning algorithms and computer hardware have led to more efficient methods for training deep neural networks (DNNs) that contain many layers of non-linear hidden units and a very large output layer known as the deep learning algorithms. Recently deep learning has been attracting a significant attention from the wide range of applications. Compare to the conventional neural networks, the key features of deep learning are to have more hidden layers and neurons, and to improve learning performance. Using these features, large and complex problems that could not be solved with conventional neural networks can be resolved by deep learning algorithms. Consequently, deep learning has been applied to various applications including pattern recognition and classification problems; for example, speech recognition [3], handwritten digit recognition [4], human action recognition [5], and so on. However, to the best knowledge of the authors, no result has been published in the automatic control field. Thus, this paper focuses on presenting the utilizing possibility of deep learning in control areas. This study was designed to mimic the PID controller using a DBN algorithm. The simulation is performed using Matlab/Simulink and the detailed results of a comparison study between the proposed deep learning controller and a PID controller was conducted to demonstrate the performance and effectiveness of the proposed algorithm. This paper is organized as follows. The deep learning is described in section 2. In section 3, the design of deep learning controller is explained. The comparison details between the proposed deep learning controller and a PID controller are presented with the simulation results are shown in section 4. Finally, a conclusion and future works follows in section 5. II. DEEP LEARNING Deep learning has many layers of hidden units and it also allows many more parameters to be used before over-fitting occurs. The generative pre-training creates many layers of feature detectors that become progressively more complex [6]. A subsequent phase of discriminative fine-tuning, using the standard back- propagation algorithm, then slightly adjusts the features in every layer to make them more useful for discrimination [6]. Thus, for deep learning, a deep architecture is used.

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Figure 1. Deep belief network framework [4].

During these procedures, the RBM which is basically composed of three layers is the core difference of the DBN algorithm compare to the conventional neural network. Further, since the RBM is an unsupervised learning, so it has no target data. Moreover, the RBM is responsible for generating the set of weight��s initial value that makes the learning better [11].The framework of the DBN algorithm is shown in Fig. 1. This figure indicates that the DBN algorithm has three steps: Step 1: the input data (the observation vector

(a) (b) (c) Figure 2. Design of deep learning controller.

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( )

1

= -

(1)

( )

1

= - + -

(2) where, is the moment of inertia of the rotor, is motor torque constant, is the armature current, is motor viscous friction constant, is electric inductance, is electric resistance, and is electromotive force constant. The simulation of the DC motor was performed in Matlab/Simulink as shown in Fig. 3. The parameter values of the considered DC motor can be found in Table I.

TABLE I. DC MOTOR PARAMETERS SETTING Parameter Value Parameter Value 0.01 0.5 0.1 1 0.01 0.01 Figure 3. Simulink block of DC motor system.

The total feedback control of DC motor based on deep learning controller in MATLAB environment is given in Fig. 4, where, the input and output of the system are voltage and angular speed , respectively.

Figure 4. Feedback control of DC motor based on deep learning controller in Matlab/Simulink.

IV. SIMULATION RESULT The simulation was conducted in two scenarios to check the performances of the proposed controller: Scenario. 1: the DC motor was excited with a simple step input; Scenario. 2: the DC motor was excited with a more complex input, the cascade step input.

Figure 5. System response using the PID controller in the scenario. 1.

0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 Time Speed Reference PID

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Figure 6. System response using the deep learning controller in the scenario. 1.

Fig. 7 shows that the residuals were big in the transient part, but after just 0.7s the residuals were nulled for both the PID and the proposed deep learning controllers. Further, the RMSE variations for both controllers were very small (~ 10-2). Thus, as shown in Fig. 7, the residual and RMSE results demonstrate the effectiveness of the proposed deep learning controller to be used as a tool to control the DC motor output, the speed.

Figure 7. The residual and RMSE variations of deep learning controller and PID controller.

Figure 8. System response using the PID controller in the scenario. 2.

Fig. 8 and Fig. 9 show that the performances of the proposed deep learning controller were almost as good as the PID controller similarly to the results of scenario 1. Further, the summary of the comparison between the PID controller and the deep learning controller are given in Table II.

Figure 9. System response using the deep learning controller in the scenario. 2. TABLE II. RMSE RESULT Method Scenario PID controller Deep learning controller Scenario 1 0.0539 0.0554 Scenario 2 0.3097 0.3659

V. CONCLUSION In this paper, a deep learning controller based on DBN algorithm was designed to explore the ability of applying the deep learning algorithm to the control problems. A comparison study between the PID controller and the proposed deep learning controller was performed to verify the feasibility of the use of deep learning in control theory. The simulation results demonstrate the effectiveness of the proposed deep learning controller to be used as a control tool. ACKNOWLEDGMENT This research was supported by the MSIP (Ministry of Science, ICT & Future Planning), Korea, under the C- ITRC (Convergence Information Technology Research Center) support program (NIPA-2014-H0401-14-1004) supervised by the NIPA (National IT Industry Promotion Agency). REFERENCES

[1] X. Zhu, C. Guan, J. Wu, Y. Cheng, and Y. Wang, "Expectation- Maximization Method for EEG-Based Continuous Cursor Control,"

0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 Time Speed Reference Deep learning 0 0.5 1 1.5 0 0.5 1 Time R es idual 0 0.5 1 1.5 0 5 10 x 10-3 Time R M SE Deep learning PID Deep learning PID 0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 Time Speed Reference PID

0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 Time

Speed

Reference Deep learning

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