# Zero Average Dynamic Controller for Speed Control of DC Motor
## 1 Introduction
Predictive control comprises establishing a predictive model to predict future output values, the definition of a cost function in terms of the output error, and the minimization of the cost function to determine the optimal control sequence. In [32], a predictive control based on a deadbeat control algorithm is proposed for a permanent magnet synchronous motor (PMSM). An improved deadbeat control scheme is proposed in order to provide robustness and improve the motor current tracking while suppressing torque ripple. In Trivedi [33], deadbeat, hysteresis based and finite-control set methods of predictive control are proposed for a PMBLDC motor in the stationary plane. In [34], a predictive control is proposed for a long-stroke planar motor for high-precision positioning applications, considering long-stroke, time-varying trajectory tracking. An additional term is introduced to the cost function. The sliding mode control (SMC) method is designed to cope with parameter variation, model uncertainties, and disturbances. In [35], a time-dependent, global, non-singular, and fixed-time terminal SMC is proposed for a second order PMSM using a time-dependent terminal sliding surface and a piecewise continuous SMC law. In [36], an SMC is designed for a PMSM drive using an improved exponential reaching law to solve the chattering problem while providing a quick output response. In [37], an SMC is proposed for the speed control of a permanent magnet linear synchronous motor (PMLSM) using a power function in the SMC strategy to suppress the conventional SMC chattering. In motor control strategies, function approximation methods, e.g., neural networks, allow approximating of the unknown nonlinear function of the dynamic model. In [38], a neural network non-singular fast terminal SMC is proposed for a PMLSM. In [39], a neural network learning adaptive robust control (NNLARC) is proposed for an industrial linear motor-driven stage. However, the ZAD control strategy has significant advantages in controlling power converters and drives, such as low stationary-state error, fixed commutation frequency, and non-saturated cycle. Therefore, in this paper, a ZAD control strategy is proposed for speed motor control of a converter-motor system. The experimental test of the buck converter driving the motor was built, and simulations were also performed. The main contributions of this paper are:  
1. A ZAD control strategy was proposed to achieve proper tracking performance in experiments and simulations, obtaining similar results in both. 2. A converter prototype was built to control the DC motor speed. This controller achieved low acoustic noise and low electromagnetic interference. In addition, it provided the possibility of defining the parameters and changing sampling frequency, switching frequency, and quantization levels of the measurements. 3. A discrete quasi-sliding mode control was used to perform a fixed commutation frequency. Thus, the voltage and current values entering the motor are less abrupt. 4. A versatile prototype was developed that uses different commutation frequencies, real-time parameter variation, and current and voltage measurements during a given time by using a trigger signal. The paper is organized as follows. The mathematical model and the control technique are presented in Section 2. The numerical simulation and experimental results of the buck converter with the DC motor (buck-motor system) using the ZAD technique are included in Section 3. Finally, conclusions are presented in Section 4.