Abstract
Training data for a deep learning (DL) neural network (NN) controller are obtained from the input and output signals of a conventional digital controller that is designed to provide the suitable control signal to a specified plant within a feedback digital control system. It is found that if the DL controller is sufficiently deep (four hidden layers), it can outperform the conventional controller in terms of settling time of the system output transient response to a unit-step reference signal. That is, the DL controller introduces a damping effect. Moreover, it does not need to be retrained to operate with a reference signal of different magnitude, or under system parameter change. Such properties make the DL control more attractive for applications that may undergo parameter variation, such as sensor networks. The promising results of robustness against parameter changes are calling for future research in the direction of robust DL control.
Highlights
Design methods for feedback control systems are well-established
We show that the addition of hidden layers, resulting in deep neural network (NN) controllers, produces a damping effect and improves feedback control system stability
The BP algorithm is based on stochastic gradient descent (SGD) learning as in the single-layer NN, but uses a different method to update the gradient, namely, backpropagation
Summary
Design methods for feedback control systems are well-established. These include classical linear control system design, techniques for nonlinear control, robust control, H-∞ control and adaptive control. We show that the addition of hidden layers, resulting in deep NN controllers, produces a damping effect and improves feedback control system stability. Relevant recent works in the literature include [8] where a NN controller with one hidden layer is trained for use with multi-input, multi-output (MIMO) systems resulting in an improvement in transient response regarding overshoot and settling time, but without resorting to DL. The deep NN controller used with a second-order plant in a closed-loop control system is more computationally efficient in the training phase as well as in real-time operation, while retaining DL benefits, compared to the above works that employ DBNs, RL and LSTMSNNs. In addition, detailed results are presented regarding improvement in settling times as the DL controller implementation gets deeper, steady state error and overshoot. There are several training algorithms for training the neural network weights, the most important being the backpropagation (BP) algorithm, in which the output error starts from the output layer and propagates backwards until it reaches the hidden layer
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