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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Physical sensors have a key role in implementation of real-time vector control for an induction motor (IM) drive. This paper presents a novel boundary layer fuzzy controller (NBLFC) based on the boundary layer approach for speed control of an indirect field-oriented control (IFOC) of an induction motor (IM) drive using physical sensors. The boundary layer approach leads to a trade-off between control performances and chattering elimination. For the NBLFC, a fuzzy system is used to adjust the boundary layer thickness to improve the tracking performance and eliminate the chattering problem under small uncertainties. Also, to eliminate the chattering under the possibility of large uncertainties, the integral filter is proposed inside the variable boundary layer. In addition, the stability of the system is analyzed through the Lyapunov stability theorem. The proposed NBLFC based IM drive is implemented in real-time using digital signal processor (DSP) board TI TMS320F28335. The experimental and simulation results show the effectiveness of the proposed NBLFC based IM drive at different operating conditions.

Vector control techniques with sensors or sensorless are very common in induction motor control applications due to their traditional superiority in high-performance applications. With the invention of the vector control technique the AC motor became popular for variable speed drives and motion control [

The SMC-based drive system has many attractive features [

In recent years, the chattering issue has become the research focus of many scholars [

To improve tracking performance considering the thin boundary layer near the sliding surface, the slope of the continuous function or boundary layer thickness is adjusted by the fuzzy inference system [

This paper applies a modified fuzzy controller to adjust the thickness of the boundary layer near the sliding surface for improving tracking performance under small uncertainties. Also, an integral filter is proposed in the variable thin boundary layer to eliminate the chattering despite large uncertainties so that the stability of the proposed NBLFC is guaranteed. The performance of the proposed NBLFC-based IM drive is tested in both simulations and experiments and also compared with the conventional BLFC and PI controller-based IM drives.

The indirect field-oriented control (IFOC) along with the rapid progress of power electronics, DSP, sensors, and control theory can be used in high performance drive applications [

The mathematical models of an IM in d-q synchronously rotating reference axis are shown in

Rotor voltage equations in

In IFOC, the rotor flux is oriented entirely in the d-axis by setting

By substituting

Considering

Considering

Considering the implementation of sensored field-oriented control as shown _{r}_{L}_{p}_{t}_{r}_{p}_{r}_{p}_{r}

To achieve the nominal model of an IM drive, the nominal value of the parameters must be considered without any disturbances [_{t}̅_{r}̅_{r}̅_{P}_{p}

In the above equation, the uncertainties are shown by ΔA and ΔB. Also unstructured uncertainty due to detuning field-orientation in the transient state and the unmodeled dynamics in practical applications are shown as

Considering the speed tracking error, _{r}_{r}^{2}

In order to achieve suitable performance despite uncertainties on the dynamic of the system (lumped uncertainty), a discontinuous term must be added to equivalent control part across the sliding surface

Therefore, favorable control performance considering uncertainties and unmodeled dynamics can be achieved by the control law as below:

Stability condition can be obtained from the Lyapunov stability theorem as [

Essentially, eliminating chattering phenomenon is done by smoothing out the control discontinuity in a thin boundary layer near to the sliding surface [

Overall, heuristic techniques are usually complex which tends to mask the simplicity of fuzzy control and contribute to time delays when attempted for real-time control [

The design of the fuzzy controller essentially consists of a knowledge-based design that includes formulation of membership function (MF) shape and its distribution of the fuzzy variables, the rule matrix design, and a number of linguistic rules. It can be shown that MFs play an important role in the performance of fuzzy control systems.

In addition, the most common approaches to FIS are the Sugeno and Mamdani approaches. In the Sugeno approach it would be difficult to give a linguistic interpretation of the information that is described in the rule base, while, the Mamdani approach is typically used in modeling human expert knowledge [

Based on the aforementioned discussion, this paper modifies an existing fuzzy controller in the literature [

Substituting

The Mamdani type fuzzy inference method with 36 rules shown in

An integral filter is designed inside the variable thin boundary layer to eliminate the chattering despite large uncertainties. To design the integral filter, the related discussions are presented as follows.

For |

Since _{r}_{r}_{r}_{r}_{r}

The cut-off frequency of the filter

In the above equation,

The variable switching

Then, the block diagram of the proposed NBLFC-based IM drive is obtained as shown in

In the above equation,

In this state, the equation of

Substituting

The polynomial roots of the filter above are obtained as:

In the above filter

The performance of the proposed NBLFC-based IM drive has been investigated extensively in simulation. In order to show the superiority the performance of the proposed NBLFC is also compared with the tuned PI and the conventional BLFC controllers under different operating condition such as a sudden change of load, change of command speed, and parameter changes.

The discrete time Simulink model with sampling time Ts = 1 × 10^{−4} s along with the digital motor control (DMC) and IQMath libraries from TI and Mathworks are used to simulate the IFOC induction motor drive. These libraries were used to optimize the Simulink blocks. The SVM-VSI type inverter is modelled based on the fast switching IGBTs model from the Simulink toolbox along with the aforementioned libraries in MATLAB. Based on the block diagram of closed-loop vector control of the IM drive shown in

For simulation tests, the following cases including parameter variations and external load disturbance are considered. If not mentioned, all other parameters are considered nominal in all the cases:

Within the restriction of the control effort, in order to achieve the system stability, and the best transient performance, the control parameters are chosen as, ^{-1}

In

Simulation results for the tuned PI, conventional BLFC and the proposed NBLFC controllers, respectively, in

In

To implement the IM drive in real-time, an ezdspF28335 platform from Spectrum Digital (Stafford, TX, USA) is employed.

As shown in

Rotor position is sensed by an optical incremental encoder (QEP) E60H20 with three output channels (A, B, and index) which must be mounted properly on the rotor shaft as shown in

The control algorithms are made by Simulink models and downloaded to the DSP board through Code Composer Studio (CCStudio) TI software. The outputs of the board are six logic signals, which are fed to the inverter (INV) through the gate drive (GD) circuit as shown in

The experimental setup for the proposed NBLFC based prototype 1 kW IM drive system is shown in

The tuned PI, the conventional BLFC, and the proposed NBLFC were simulated to search for the controller which provides the best dynamic performance. Through simulation tests it was found that the proposed NBLFC provides the best dynamic performance. To validate the simulation results, the proposed controller is implemented in real-time and compared with the conventional BLFC and the tuned PI controller based IM drive. As the PI controller has been utilized widely in the industry, it was considered as the benchmark controller. For the experimental test verifications, the following cases are considered. If not mentioned, like in the simulation results, all other parameters are considered nominal in all the cases:

It is noteworthy that the PI parameters in practice, are found as, Kp = 0.8, Ki = 0.0002, and Kc = 0.0002. In

In

A novel boundary layer fuzzy controller-based IFOC of an IM drive has been presented in this paper. The structure of the proposed controller is based on e smoothing out the control discontinuity in a thin boundary layer near the sliding surface. The proposed fuzzy system based on the variable boundary layer has been employed to adjust the thickness of boundary layer near the sliding surface to improve tracking performance under small uncertainties. To eliminate the chattering despite large uncertainties, an integral filter has been used in the variable thin boundary layer so that the stability of the proposed NBLFC is guaranteed. The proposed NBLFC-based IM drive has been successfully implemented in real-time using an ezdspF28335 DSP board and physical sensors for a prototype 1.5 HP motor. The appropriate utilization of the current and position sensors has been contemplated. The performance of the proposed NBLFC has been tested in both simulation and experiment. The performance of the proposed NBLFC controller was found superior to the conventional PI and SMC controllers under different operating conditions such as a step change in command speed, load disturbance and parameter variations over a wide speed range. Furthermore, the proposed NBLFC has reduced the steady-state chattering in current. Thus, the proposed NBLFC ensures less harmonic loss and associated heat dissipation in the motor.

This research is supported by the University of Malaya (UM) High Impact Research Grant UM.K/636/1/HIR (MOHE) /ENG22 from the Ministry of Higher Education Malaysia.

The authors declare no conflict of interest.

Friction factor

Sliding surface coefficient

Digital Motor control

Digital signal processor

Error between actual and command speed

Generator

Gate drive

Positive constant for sliding surface

Interface circuit

Inverter

_{a}

_{b}

_{c}

Three phase current

_{αs}

_{βs}

Stationary frame stator currents

Synchronous frame stator currents

Synchronous frame rotor currents

_{r}

Inertia of rotor

_{d}

Desired control gain

Lumped uncertainty

_{m}

Mutual inductance

_{s}

_{r}

Stator and rotor inductance, respectively

Motor

Number of poles

Optical incremental encoder

Revolutions per minute

_{s}

_{r}

Stator and rotor resistance, respectively

Saturation function

_{S}

Time-varying surface

Sign function

Space vector modulation

_{e}

Electromagnetic torque

_{L}

Load torque

_{reach}

Reaching phase

Control effort

_{eq}

Equivalent control

_{r}

Reaching control

Voltage source inverter

Lyapunov function

_{αs}

_{βs}

Synchronous frame stator voltages

Synchronous frame rotor voltages

Synchronous frame stator voltages

First derivative of

Second derivative of

Command value of

Absolute value of

Synchronous frame stator fluxes

Synchronous frame rotor fluxes

Differential operator

_{e}

_{r}

Synchronous speed and rotor speed, respectively

_{sl}

Slip angular frequency

Total leakage factor,

_{r}

Rotor position

_{e}

Synchronous position

Alteration of switching variable

Change of speed error

Integral constant time of system

Boundary layer thickness

Positive constant of stability threshold

Cut-off filter frequency

Block diagram of a closed loop sensord IFOC based IM drive.

Block diagram of simplified IFOC of IM.

Inputs and output membership function.

The control block diagram of the proposed NBLFC-based IM drive.

The integral filter inside boundary layer.

The main Simulink model for the IFOC of an IM drive.

Simulated speed responses-based IM drive at no load in

Simulated q-axis current responses-based IM drive at no load in

Simulated speed responses-based IM drive in

Simulated q-axis current responses-based IM drive in

Simulated speed responses based IM drive in

Simulated q-axis current responses-based IM drive in

Simulated tracking error responses-based IM drive in

Block diagram of the hardware schematic for real-time implementation of VSI fed IM drive.

Connection of encoder for IM drive.

Experimental setup of the proposed IM drive.

Experimental speed responses-based IM drive in

Experimental q-axis current responses based IM drive in

Experimental speed responses-based IM drive in

Experimental q-axis current responses-based IM drive in

Fuzzy rule based matrix for NBLFC.

Alteration of switching variable amplitude | Δs(t)| | Z | S | M | MB | L | VL | |

Z | VL | VL | L | L | MB | MB | |

S | VL | L | L | MB | MB | M | |

M | L | L | MB | MB | M | M | |

MB | L | MB | MB | M | M | S | |

L | MB | MB | M | M | S | S | |

VL | MB | L | M | S | S | Z |

Induction motor parameters.

Rated power | 1,000 W | Rated torque | 3.37 NM |

_{s} |
6 | _{r} |
0.0055 Kg.m^2 |

_{r} |
5.72 | 0.001 Kg.m^2/s | |

_{s} |
428.7e-3H | 2 | |

_{r} |
428.7e-3H | Rated speed | 2830 RPM |

_{m} |
416.6e-3H |