The derivation of a mathematical model for traveling wave ultrasonic motors and its experimental validation are reported. In a first step, the motor was structured into subsystems and models for the individual components were derived, simplified and described mathematically. The resulting submodels were then joined into an overall unified model of the motor, which allows us to study the impact of diverse motor parameters and control variables on the motor performance. In order to validate the model, systematic simulations with properly selected parameters were performed and compared with measurement results obtained from an actual traveling wave ultrasonic motor. Very good correspondence between model predictions and real motor behavior was observed. The validated model can be used in the design of traveling wave ultrasonic motors to optimize the performance by choosing the 'right' motor and control parameters at an early design stage.

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This paper describes the application of adaptive predictive expert (ADEX) control methodology to the oxidation ditch reactor in the wastewater treatment plant of Ceutí (Murcia, Spain) and evaluates the performance of the ADEX control system against that of the previous control system operating the plant. After a basic description of ADEX control methodology, the ditch reactor is described, as well as the control objectives and the control strategy, which focused on energy consumption reduction. The results of the application of the ADEX control system show significant improvement compared with the previous control system in terms of higher stability and precision of controlled variables, reduction of energy consumption of the plant, and better quality of the effluent water. Figure 4, the upper plot of Figure 7 shows the trend curves and operational limits of the redox in both reactors; the middle plot shows the evolution of the DO in both reactors and the common set point. The third plot shows the gate valve openings. As inThe ADEX controllers used during the nitrification phase to control the DO in the biological reactors, operated in an AP domain, and their sequence of calculations was basically that described in Section 2.2. These were single-input single-output controllers with a control period of 15 s and an AP model described by Equation (3), that is, two Ǫ i .k/ and three O b i .k/ parameters. The driver block dynamics were consistent with those of a second-order model with damping ratio equal to one and time constant equal to one control period. The performance of these controllers is illustrated by the results presented in Figures 7 and 8 and discussed in the next section. Figure 8. Dissolved oxygen control redox evolution during one nitrification/denitrification cycle.The dynamics in one nitrification/denitrification cycle is shown in more detail in Figures 8 and 9. The upper plot of Figure 9 shows the trend curves of the mean position deviation variable o and its set point; the second plot shows the pressure in the common collector and its set point, and the third, the evolution of the frequency converter of the blower. DISCUSSION OF THE RESULTSThe Ceutí WWTP currently operates with a wastewater flow of 3000 m 3 /day that is considerably lower than the designed wastewater flow. A single blower is therefore sufficient to provide the Figure 9. Pressure evolution during one nitrification/denitrification cycle.

In this paper we present the application of adaptive predictive expert controllers to dissolved oxygen (DO) control in the aerobic reactors of a wastewater treatment plant. The control system described in this paper consists of adaptive predictive expert control loops complemented by optimisation logic. The controllers successfully cope with nonlinearity and changing operating conditions of the process by predicting the evolution of the controlled variable and adapting to changes in the process dynamics. This results in more precise and stable DO control, offering many benefits. The complementary optimisation logic maintains the air pressure in the common collector at the lowest possible level, enabling adequate DO control and thus considerably reducing energy consumption.

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