This paper presents a design and real-time application of an efficient Artificial Intelligence (AI) method assembled with PID controller of an eddy current dynamometer (ECD) for robustness due to highly nonlinear system by reason of some magnetism phenomena such as skin effect and dissipated heat of eddy currents. PID Control which is known as the most popular conventional control method in industry is inadequate for such nonlinear systems. On the other hand, Adaptive Neural Fuzzy Interference System (ANFIS), Single Hidden Layer Neural Network (SHLNN), General Regression Neural Network (GRNN), and Radial Basis Neural Network (RBNN) are examples used as artificial intelligence-based techniques that can increase the performance of conventional control systems in particular. The proposed control system proves changeable _{p} (Proportional gain), _{i,} (Integral gain) and _{d} (Derivative gain) parameters in real-time to adapt and presents a good capacity to adapt nonlinearities and bring robustness using 4 different versatile soft computing methods of ANFIS, SHLNN, GRNN, and RBNN. The testing dataset is extracted from experimental studies and its robustness has also been verified with different Artificial Intelligence (AI) methods. The presented technique is observed to have a good performance in terms of response time (t) and accuracy of desired speed value (V) under different parameters such as non-linear dynamics (V, T) of the system elements and the varying load effects.

The automotive companies have been using the Eddy Current Dynamometers (ECD) as an auxiliary braking system, especially for engine testing and analyzing operations. The operational principle behind this brake system is based on the electromagnetic induction theory called “Eddy Current” phenomenon. The Eddy Currents are generated at the moment when a conductive material moves inside a magnetic field. These currents generated on the conductive material as a result of the magnetic field interaction are formed as circles due to the inexact way to move. The circles unite and create eddies on the moving material. The Eddy Currents emerge a magnetic field against the magnetic field of coils that concludes a force opposes motion. The Eddy Currents are one of the most undesirable things for many applications such as AC motors. The fundamentals of Eddy Current dynamometers are discovered by Faraday i.e., the Faraday induction law [

The most severe drawback of the eddy current dynamometer is the huge amount of excitation current that may lead to serious safety issues. In addition, there may be other problems including skin effect, demagnetization effect, excessive magnetism [

In literature, many studies focus on the control strategies of Eddy Current Brakes. Tan et al. [

Many researchers have examined Artificial Intelligence-based PID control. Jin et al. [

Experiments were conducted in the Eddy Current Dynamometer rig located in the laboratories of Automotive Engineering Department at Cukurova University. The mechanical system consists of several parts that are illustrated in

The Eddy Current Dynamometer assemble is joint at a contact point. The contact point unites the rotor and stator which carries the load cell and the coils that conduct the magnetic field. The rotor is mounted to a connecting shaft, the IC engine, Eddy Current Brake and encoder as visualized in

The Eddy Current Brake is used to generate the stopping effect on testing system (IC engine, Electric motor etc.) for controlling the speed of the torque shaft. The Eddy Current Dynamometer is used to simulate operating conditions of motor applications, motor control research and production, repair tests. In this study, Telma brand retarder is used that has a linear braking force ranging between 0 and 1000 rpm values. At higher speeds, braking torque acts nonlinearly as the nature of the magnetic field results in skin effect, demagnetizing effects, and less time for inducing eddy currents. The details of the experimental setup are illustrated in

The power supply of Eddy Current Brake has a capacity of PWM output of 80 A with 256 resolutions. This means the control signal defined a specific value that is between 0 and 256. A PC with Intel i3 microprocessor (3.9 GHz) and 16 GB RAM is utilized to carry out the calculations required for the control signal and artificial intelligence calculations in MATLAB/Simulink environment. The calculated control signal is sent by the Microcontroller Unit (MCU) card to the eddy current driver that can run 100 A, 2400 W devices. The MCU card is selected as Arduino Mega 2560 due to its versality and MATLAB/Simulink linking ability. The speed of the shaft is measured with a line drive magnetic encoder with a resolution of 360 (pulse/rotation). Meanwhile, a load cell and contactless infrared temperature sensor are also used in the sensory system.

In order to find out the capabilities of the magnetic retarder, system identification and parameter estimation tasks have to be done. The parameters of shaft speed and rotor temperature have a huge effect on the braking performance of the retarder. Hence, the system behaviors can be predicted with respect to speed and temperature changes.

The Eddy Current Dynamometers are naturally nonlinear since their braking torque changes unpredictably with rotor speed and rotor temperature. It is well known torque produced by eddy current brake is related to conductivity of the rotor as seen on

where σ is conductivity of rotor and T_{b} is produced torque. Heating occurs during the braking process leads to increase in the rotor temperature. Hence, the conductivity of metal rotor decreases irregularly at the same time as temperature increases. In this regard, hotter rotor causes less torque produced based on a nonlinear manner. To determine the nonlinear performance of the system, the step response of the eddy current dynamometer speed against PWM load has been tested for 1800–3000 rpm range with a resolution of nearly 100 rpm. In addition to speed, the temperature of the Eddy Current Dynamometer rotor is measured at 4 different values between 25 and 100°C for each speed measurement. The results of each step response experiment yield graphs which can lead us to linearize the system and determine _{p}, _{i,} and _{d} values using the highest slope of the graph (

PID is a control method that combines proportional, integral, and derivative of the input error, helping the unit to automatically compensate for changes as seen in

The main advantage of PID control is the wide application areas including mechanical systems, hence in most engineering applications as commonly accepted, PID control is proved to be the most suitable control method [

Biological nervous systems and mathematical systems’ learning theories inspired the Artificial Neural Network (ANN) systems. The learning procedure of ANN is achieved by various mesh of processing nodes and connections. Neural Networks are simply defined as massively parallel interconnected networks of simple (usually adaptive) elements. Their hierarchical organizations are intended to interact with objects of the real world in the same way as biological nervous systems do [

In this study, Neural Fitting (

There are various types of NNs for use of different purposes in literature. One of them is Generalized regression neural network (GRNN). A GRNN is suitably designed for function approximation purposes. [

Radial basis neural networks (RBNN) have advantages of easy design, good generalization, strong tolerance to input noise, and online learning ability [

ANFIS word comes from Adaptive Neuro-Fuzzy Interference System. ANFIS builds a Fuzzy Interference System (FIS) using a selected input/output data block. FIS membership function parameters are adjusted (tuned) with help of the back-propagation algorithm or hybrid version of the least square method and back-propagation algorithm. Hence, the tuning process lets the Fuzzy systems learn from the input/output data block.

FIS is one of the most popular artificial intelligence methods. It is solely based on human expert experience to make a decision. Therefore, the success of FIS decisions is related to either the accuracy of experts or converting these experiences from real-world to fuzzy logic interface [

The main advantages of ANFIS are [

ANFIS can design nonlinear functions of arbitrary complexity using data blocks.

ANFIS can be coupled with conventional control techniques.

In this paper, ANFIS and PID conventional control techniques are augmented. The convergence of results is performed by the Mean Average Percent Error (MAPE) given by

Here,

MAPE, % | Evaluation |
---|---|

MAPE ≤ 10% | High accuracy forecasting |

10% < MAPE ≤ 20% | Good forecasting |

20% < MAPE ≤ 50% | Reasonable forecasting |

MAPE > 50% | Inaccurate forecasting |

_{p}, _{d,} and _{i} values separately.

A SHLNN, an ANFIS, a GRNN, and a RBNN structures are constructed based on system dynamics and previous studies. The gathered experiment results prove that the training algorithm of backpropagation is substantially satisfactory for predicting _{p}, _{d,} and _{i} for various shaft speeds (V), Eddy Current Brake rotor temperature (T),

The SHLNN, ANFIS, GRNN, and RBNN predictions for Eddy Current Dynamometer achieved quite successful results against test data that are represented in _{p} value, the amount of training hidden neuron number of SHLNN is 10, and the training algorithm is Levenberg–Marquardt. 61 rows of input data are presented randomly while 70% (42) of input data is used for training job, 15% (9) is used as validation job, lastly, 15% (9) is used as testing. 8 selected data left are used for testing of built SHLNN structure.

Test values for _{p} have an interval of 102.45 and 67.78. MAPE values are found as 0.43 for all steps after 19 epochs. Also, designed ANFIS for _{p} has an amount of training membership function of 3 for each input resulting and 12 input _{p}, _{d}, and _{i} with 61 training data and 8 test data. Finding the correct spread value is accomplished using trial and error method. Mean squared error goal of RBNN is always picked as 0. Optimum MAPE results of RBNN for _{p} were found as 0.18 at 250 spreads. On the other hand, GRNN has a relatively lower performance with best MAPE value of 8.66 at 50 spreads even it is under the limits of successful estimation according to

The _{i} value for test data varies between 8.84 and 13.2. The training parameters for the _{i} value of the SHLNN were determined using 61 lines of input data, the number of hidden neurons was 10 and the training algorithm was Levenberg–Marquardt. Of the input data 61, 70% (42) is used for training work, 15% (9) as validation work, and finally 15% (9) as testing. 8 different data are spared for testing of built SHLNN structure. The best MAPE value was observed as 1.70 in the 9th epoch. Also, the number of nodes of the ANFIS system, which is established with 81 fuzzy rules and 12 input

_{d}. The SHLNN has hidden neuron number of 10 and training algorithm of Levenberg–Marquardt, presented 61 rows of input data while 70% (42) of input data is used for training job, 15% (9) is used as validation job, lastly, 15% (9) is used as testing. Testing of built SHLNN structure is done with 8 selected data from test set. MAPE value is found as 3.04 after 85 epochs. Secondly, 3 training membership functions for each input resulting in 81 Fuzzy rules and 12 input _{d}, 3.43 at 18 spreads, and 0.13 using RBNN at 50 spreads. ANFIS, GRNN, and RBNN structure are built using 61 sets as training data and 8 sets as testing data.

Eventually, the results show that SHLNN, ANFIS, GRNN, and RBNN training procedures have been predicted successfully for the _{p}, _{i} and _{d} values. A comprehensive study is done and the results are discussed in detail in _{p}, _{i} and _{d} parameters are provided from AI subsystem and error is calculated by difference of the shaft speed and reference value as pictured in

_{p} |
_{i} |
_{d} |
||
---|---|---|---|---|

Test data | SHLNN | 0.43 | 1.70 | 3.04 |

ANFIS | 1.09 | 0.93 | 0.93 | |

GRNN | 8.66 | 3.99 | 3.43 | |

RBNN | 0.86 | 0.01 | 0.13 | |

Training data | SHLNN | 0.192 | 0.29 | 0.0003 |

ANFIS | 0.036 | 0.004 | 0.004 | |

GRNN | 6.80 | 6.23 | 6.23 | |

RBNN | 0.012 | 1.49591.10^{–8} |
1.03.10^{–10} |

_{p}, _{i}, and _{d} has an interval of 4.61 and 4.88, 12.66 and 13.82, 3.16 and 3.45, respectively. Therefore, ECB braking load calculated using these parameters. At the end of the test, adaptive PID algorithms pause and magnitude of the parameters alter and rotor dissipates heat and decrease temperature consequently.

Eddy Current Dynamometers are electrically excited, non-contact brakes especially used for heavy-duty vehicles, and internal combustion engine testing with complications to control due to nonlinearities. In this paper, SHLNN + PID and ANFIS + PID GRNN + PID, and RBNN + PID control methods are examined for Eddy Current Dynamometer (ECD). For the _{p}, _{i}, and _{d} values the most accurate algorithms are SHLNN + PID, RBNN + PID, and RBNN + PID with MAPE values of 0.43, 0.01, and 0.13, respectively. In this study, ideal NNs and the best PID parameters were found to be used in experimental studies. Therefore, the offered system is proven to be very useful as a tool for determining the correlation and also to control of Eddy Current Dynamometers. It also gives an accurate and simple approach in the analysis of this nonlinear, multivariable problem—that is, the robustness of the Eddy Current Dynamometer parameters.

I would like to acknowledge TEMSA and BAŞAK Truck Companies for their dynamometer, and IC engine grants.