# Robust Speed Tracking of Induction Motors: An Arduino-Implemented Intelligent Control Approach +
## 1 Introduction  
Induction machine (IM) drives [1; 2] have been widely utilized in motion control applications such as the speed control of a pump, or a machine tool, or an electric vehicle, etc. (e.g., [3; 4]). To achieve high servo quality, many studies (e.g., [5; 6]) have been focused on the speed control of a direct-field-oriented (DFO) IM. However, additional design efforts for decoupling the torque and flux control of a DFO IM are required. Additionally, the decoupling control is vulnerable to adverse load disturbances and parameter variations which can severely degrade tracking performance. In comparison, the speed controller design for a voltage/frequency (V/f) controlled IM is generally much simpler than that for a DFO IM. Accordingly, this paper adopts a V/f controlled IM framework for speed control. In motion control applications, it is desirable that a controlled IM should closely follow a reference speed trajectory in situations with or without torque disturbances. Though the system stability may be guaranteed by using the conventional proportional-integral (PI) or proportional-integral-derivative (PID) speed controllers (e.g., [7]) with well-chosen parameter values, the robustness to abrupt load changes in the motor may not be improved. This difficulty may be overcome by using a model-based predictive control strategy (e.g., [5; 6; 8]), an adaptive backstepping method (e.g., [9]), a descriptor approach (e.g., [10]), a composite nonlinear feedback control scheme (e.g., [11]), or aH\({}^{\infty}\) output-feedback control method (e.g., [12]). However, the control performance relies on how well the system is described by the model. Accordingly, the incorporation of machine intelligence into the control of IM drives has been widely used as a viable alternative for improving the system stability, performance and robustness. Specifically, intelligent controllers for IM drives have been proposed based on fuzzy logic (e.g., [13; 14; 15]) or neural networks (e.g., [16]) or neuro-fuzzy inferences (e.g., [17; 18; 19]) or a particle swarm optimization algorithm (e.g., [3]). Based on the use of a fuzzy controller for adaptively adjusting PID parameter values, a fuzzy P+ID controller in [20], a fuzzy PI self-tuning controller in [21; 22; 23] and a fuzzy self-tuning fuzzy PID controller in [24; 25] may also be employed. In addition, a fuzzy model-based predictive control strategy (e.g., [26]) may be utilized. Nevertheless, the aforementioned controller structures did not investigate a control scheme composed of a fixed-gain PI or PID in combination with a fuzzy-logic controller (FLC). Thus, a Ziegler-Nichols (Z-N) PID (e.g., [27]) in tandem with a FLC was proposed in [28] for the control of a DFO IM. Unlike best trial-and-error PI or PID controllers, the foregoing intelligent controllers can adaptively mitigate the adverse effects of torque disturbances and achieve desirable performance. The first objective of this paper is to present an intelligent control scheme which has simple design and satisfactory performance for robust speed control of a V/f controlled IM. In this regard, we propose a modified Z-N PID+Fuzzy controller, which consists of a fixed-gain modified Z-N PID in [29] together with an FLC. Our proposed approach is distinct from other schemes (e.g., [30; 31; 32]). The modified Z-N PID is adopted because it can outperform the Z-N PID. Like the Z-N PID+Fuzzy in [28], the modified Z-N PID and the FLC of the proposed controller are connected in tandem. We design an adequate FLC, distinct from the FLC in [28; 33] in membership functions, based on the output signal of the modified Z-N PID. The FLC gives adequate torque commands which in turn yield appropriate stator frequency commands for controlling the speed of the IM. Meanwhile, the FLC does not tune PID parameter values. The second objective of this paper is to feasibly achieve low-cost control implementation.