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Efficient identification and control algorithms are needed, when active vibration suppression techniques are developed for industrial machines. In the paper a new actuator for reducing rotor vibrations in electrical machines is investigated. Model-based control is needed in designing the algorithm for voltage input, and therefore proper models for the actuator must be available. In addition to the traditional prediction error method a new knowledge-based Artificial Fish-Swarm optimization algorithm (AFA) with crossover, CAFAC, is proposed to identify the parameters in the new model. Then, in order to obtain a fast convergence of the algorithm in the case of a 30 kW two-pole squirrel cage induction motor, we combine the CAFAC and Particle Swarm Optimization (PSO) to identify parameters of the machine to construct a linear time-invariant(LTI) state-space model. Besides that, the prediction error method (PEM) is also employed to identify the induction motor to produce a black box model with correspondence to input-output measurements.

One of the fundamental processes of control is the parameter identification. In control engineering a lot of effort has been done to develop methods to identify the system model and its parameters. A wide range of techniques such as the least squares method, the maximum likelihood method, and the cross correlation method, exist for system identification [

The Artificial Fish-Swarm Algorithm (AFA) and the Particle Swarm Optimization (PSO) are two kinds of typical Swarm Intelligence methods [

In order to guide the evolutionary-based stochastic algorithms, a novel optimization method, the Cultural Algorithm (CA) proposed by Reynolds in 1994 was developed to demanding problems, due to its flexibility and efficiency [

Culture algorithm framework.

The motivation behind this work is twofold. Firstly, in the literature there seems to be no results on hybrid AFA and CA. The knowledge stored in the belief space do act as a significant role in the process of evolution, and we try to find a proper framework for updating the belief space in combining the CA and AFA. Secondly, the new hybrid algorithm is applied to identify the parameters of a new kind of actuator, which is used to suppress rotor vibrations of an electronic machine.

As part of our investigation, two typical kinds of knowledge in CA, the situation knowledge and the normative knowledge, are stored in the belief space to update the population space and to establish the relationship between the two spaces in the CA. The performance of the CAFAC is explored using offline parameter identification of the actuator-rotor system in an electrical machine. The identification is performed based on a lower-order physical linear time invariant (LTI) parametric state-space model of the actuator-rotor system. The resulting model can be utilized to design model-based active control algorithms for vibrations reduction.

The rest of this paper is organized as follows. Section

We examine a two-pole cage induction motor equipped with a built-in force actuator, which actively generates force on the rotor (Figure

(a) The test motor [

The most important measurements for the identification are obtained using eddy current sensor. The sensors, conforming to the control signals, measure the rotor position also in horizontal and vertical directions. With them it is possible to record the rotor movement in any conditions accurately. Another set of sensors has been added on the right side of the motor in order to improve accuracy. Another important measurement devise is the encoder that provides the rotational angle and frequency of the rotor.

In the identification measurement the motor was operating at 32.085 Hz and the excitation input (control voltages in horizontal and vertical directions) was a uniform random number signal with frequency content up to 500 Hz. The output data was then processed so that the effects of vibrations were removed and only the response to the excitation signals remained [

The response to control voltages in

The data from this setup is used to obtain a mathematical actuator model that can be used for control design purposes, when the objective is compensating rotor vibrations. The motivation of obtaining a new parametric physical model is increased understanding of the model compared to a black box model, which has been used before successfully [

The linear time-invariant parametric (LTI) model of the system will be discussed. The model for the induction motor according to [

Parameters in the electromechanical model.

Parameter | Unit | Explanation |
---|---|---|

mΩ | The resistance of the control winding. | |

mH | The inductance of the control winding. | |

N/(A | The eccentricity coupling factor of the control winding multiplied with the complex conjugate of the first air-gap field harmonic [ | |

mH | Mutual inductance of rotor cage and control winding multiplied by itself and divided by rotor cage inductance of four-pole harmonic | |

1/s | ||

Wb/m | The eccentricity coupling factor of control winding multiplied with first air-gap field harmonic. | |

A coefficient related to the unbalanced magnetic pull towards the shortest air-gap (gap between stator and rotor) [ | ||

N/(m | The coupling factor of rotor cage multiplied with the complex conjugate of the first air-gap field harmonic and divided by rotor cage inductance of four-pole harmonic. | |

Wb/m | The eccentricity coupling factor of rotor cage four-pole harmonic multiplied with the first air-gap field harmonic and divided by rotor cage inductance of four-pole harmonic. |

Following [

Equation (

Rearranging this will give the rest of the matrices, which are needed for the combined model

These matrices and the mechanical model (

The parameters of the electromechanical model are listed in Table

Suppose that the problem under consideration has

The current state of the artificial fish is

The current state of the artificial fish is

The current state of the artificial fish is

Here, the fish swarm is regarded as the population space, where the domain knowledge is extracted from. Then the domain knowledge is formed and stored in belief space so as to model and impact the evolution of the population at iteration. In four versions of CAFAC, we use the situation knowledge and the normative knowledge to guide the direction and the step size of the evolution. Both of them can be depicted as follows.

The situational knowledge provides a set of best individuals available for the interpretation of specific individual experience [

The normative knowledge can give the feasible solution space of the optimization problems under consideration [

Formulation for normative knowledge updating.

where the

The acceptance function determines which individuals and their performances can have impact on the knowledge in the belief space. The number of the individuals accepted for the update of the belief space is obtained according to the following function [

The belief space can influence the evolution in the population space in three ways:

determining the step size of the evolution,

determining the direction of the evolution,

determining the visual distance of AFA.

More precisely, if the normative knowledge is used to determine the step size of the evolution and visual distance in AFA, our knowledge-based AFA is named as CAFAC (Ns). In four versions of CAFAC, all of the behaviours, preying, swarming, and chasing, are modelled by the knowledge. The influence function for the CAFAC is defined as in Tables

Influence function for swarming.

Swarming | ||
---|---|---|

Ns | ||

Sd | ||

NsSd | ||

NsNd |

Influence function for preying.

Preying | |
---|---|

Select next state (Ns, NsSd, NsNd) | |

Ns | |

Sd | |

NsSd | |

NsNd | |

Ns | |

Sd | |

NsSd | |

NsNd |

Influence function for chasing.

Chasing | |
---|---|

Ns | |

Sd | |

NsSd | |

NsNd |

If the situational knowledge is used to guide the direction of the evolution, our knowledge-based AFA is named as CAFAC (Sd).

If the normative knowledge guides the step size and the visual distance meanwhile the situational knowledge is used to determine the direction of the evolution, respectively, our knowledge-based AFA is named as CAFAC (Ns+Sd).

If the normative knowledge is used to determine the step size and direction of the evolution and the visual distance, our knowledge-based AFA is named as CAFAC (Ns+Nd).

In Tables

A criterion is set up to judge whether the algorithm falls into local optimum:

In the identification process we disturb the system by voltage

Here we use an indicator of fit value to evaluate the accuracy of an identified model for a specific parameters vector

In our previous work, we found that the NsSd version has better performance than the three others we mentioned in Section

Set all the values for the parameters and initialize the

Evaluate all the artificial fishes using the fitness function

For each

Update the belief space.

If the crossover criterion is satisfied, apply the crossover operator to the

Switch to PSO until the termination criterion is satisfied.

Switch to (3) until the termination criterion is satisfied.

End the program if the final termination criterion is satisfied.

The termination criterion here is the same as (

In PEM identification the general idea is to produce a model that minimizes a norm, such as

With the identification data, the PEM identification will result in fit values of 79.1 and 80.6 in horizontal and vertical directions. The CAFAC identification produced a model that had fit values of 73.9 and 77.7. Figure

Measured data and modelled outputs using PEM and CAFAC identification methods.

The obtained model was tested in simulations by implementing a state observer and a linear quadratic controller (LQ) for the model. The same was done in [

The estimation error of the observer in

Rotor displacement with the CAFAC model when control is switched on after 3 seconds.

It is also necessary to consider the control signal because the test equipment can produce voltages in the range of ±100 V, and naturally the voltage levels should not be very high in a properly working controller. Figure

Control voltage of the LQ controller with CAFAC model when control is switched off after 3 seconds.

The same simulations were also done with the black box model, which was identified using PEM, and the controller was tuned in the same manner. In this case the controller reduced vibrations in the simulations by 70.0% and 64.2%. The result is displayed in Figure

Rotor displacement with the PEM model when control is switched on after 3 seconds.

Control voltage of the LQ controller with PEM model when control is switched on after 3 seconds.

In this paper, we used a knowledge-based Artificial Fish-Swarm optimization algorithm to identify the parameters of an actuator model in an electrical machine. The culture framework was invested to direct the crossover operation in the AFA. In the culture framework, the situation knowledge and the normative knowledge were employed to guide the evolution of the Artificial Fish-Swarm optimization. The crossover operation can help the artificial fish jump out of the local optimum without losing the characteristics of the previous generation. The proposed knowledge-based Artificial Fish-Swarm optimization can improve the performance of the original Artificial Fish-Swarm optimization and can be applied, for example, to find parameter values for a model of an actuator used for vibration control of rotor in an induction motor. Realistic values for the components of a structural first-principles electromechanical model were obtained, which improved the earlier identification results considerably. The results compared well with those obtained by PEM identification, but because the latter does not provide physical parameter values, the method presented in the paper can be considered an improvement. Also, the nature-inspired evolutionary algorithms considered are particularly interesting, because they are computationally effective and reasonably easy to understand. Also, they do not need computation of gradients. For the future works, a time-varying model must be considered. In order to do that, more knowledge in the culture framework should be invested and more swarm intelligence must be tested to succeed in parameter identification.

This research work was funded by the Academy of Finland under Grants 135225 and 127299 and the NSFC under Grant no. 60874084.