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Figure 1. The experimental setup A detailed description of a nonlinear model of an EVF is shown in the cited literature [12] and this model has been used in this paper. The experimental setup, which is shown in Fig.1, includes the following instruments: (1) a multimeter; (2) an oscilloscope; (3) a DC power supply for sensors; (4) a control unit with an insulated-gate bipolar transistor (IGBT) converter; (5) digital scales; (6) an actuator and (7) an inlet hopper with shutter. Ihe entire system 1s powered by a main power of 220V/50Hz. The IGBT converter generates an excitation current of EVA on the principle of pulse-width modulation (PWM). The EVA transforms electromagnetic energy into kinetic energy of the vibrating trough. The flow of material from the inlet hopper to the vibratory trough takes place gravimetrically and is controlled using a shutter. The control unit uses signals from the following sensors: an acceleration sensor mounted on the base plate of the vibrating trough; a displacement sensor of the trough; a force sensor of the weighed material and a current sensor. All signals are monitored on an oscilloscope. The acceleration sensor (P/N 123-215) was attached to the vibratory trough. The control unit uses the signal from this sensor to monitor the amplitude and frequency of oscillation. The displacement sensor TURCK NI10-M18-LiU) was mechanically fastened to the base. The signal at the output of this sensor is proportional to he distance of the trough relative to the base. The mean value of the coil current is measured by a digital multimeter MZ8268). The current sensor (AS712T) is used for monitoring current with the oscilloscope (GDS-1052-U). The GBT converter is controlled by the control unit, based on the reference value of the excitation frequency and excitation power parameter (A[%]), the measured value of the flow of material through the trough ( Q,[kg/sec]) and the EVA coil

Figure 1 The experimental setup A detailed description of a nonlinear model of an EVF is shown in the cited literature [12] and this model has been used in this paper. The experimental setup, which is shown in Fig.1, includes the following instruments: (1) a multimeter; (2) an oscilloscope; (3) a DC power supply for sensors; (4) a control unit with an insulated-gate bipolar transistor (IGBT) converter; (5) digital scales; (6) an actuator and (7) an inlet hopper with shutter. Ihe entire system 1s powered by a main power of 220V/50Hz. The IGBT converter generates an excitation current of EVA on the principle of pulse-width modulation (PWM). The EVA transforms electromagnetic energy into kinetic energy of the vibrating trough. The flow of material from the inlet hopper to the vibratory trough takes place gravimetrically and is controlled using a shutter. The control unit uses signals from the following sensors: an acceleration sensor mounted on the base plate of the vibrating trough; a displacement sensor of the trough; a force sensor of the weighed material and a current sensor. All signals are monitored on an oscilloscope. The acceleration sensor (P/N 123-215) was attached to the vibratory trough. The control unit uses the signal from this sensor to monitor the amplitude and frequency of oscillation. The displacement sensor TURCK NI10-M18-LiU) was mechanically fastened to the base. The signal at the output of this sensor is proportional to he distance of the trough relative to the base. The mean value of the coil current is measured by a digital multimeter MZ8268). The current sensor (AS712T) is used for monitoring current with the oscilloscope (GDS-1052-U). The GBT converter is controlled by the control unit, based on the reference value of the excitation frequency and excitation power parameter (A[%]), the measured value of the flow of material through the trough ( Q,[kg/sec]) and the EVA coil

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Figure 2. The flow characteristic depending on frequency and average value of the EVA current (J.), fr = 51.5 Hz, A = 50%, simulation Fig.2 shows the dependence of the bulk material flow and average value of the EVA current on the EVA current frequency (f[Hz]), obtained by simulation. The mathematical model refers to an EVF with an excitation frequency equal to the mechanical resonant frequency (f,,,{Hz]). For this reason, the flow characteristic is only valid for excitation frequencies that are near the resonant frequency.
Figure 2. The flow characteristic depending on frequency and average value of the EVA current (J.), fr = 51.5 Hz, A = 50%, simulation Fig.2 shows the dependence of the bulk material flow and average value of the EVA current on the EVA current frequency (f[Hz]), obtained by simulation. The mathematical model refers to an EVF with an excitation frequency equal to the mechanical resonant frequency (f,,,{Hz]). For this reason, the flow characteristic is only valid for excitation frequencies that are near the resonant frequency.
Figure 3. The flow characteristic depending on frequency and average value of the EVA current (J.), fnr = 51.5 Hz, experimental results Fig.3 shows experimental results of measuring the flow of bulk material and the average value of the EVA current depending on the frequency of the EVA current pulses.
Figure 3. The flow characteristic depending on frequency and average value of the EVA current (J.), fnr = 51.5 Hz, experimental results Fig.3 shows experimental results of measuring the flow of bulk material and the average value of the EVA current depending on the frequency of the EVA current pulses.
Figure 4. The transmission characteristics of the EVF for displacement P [mm]
Figure 4. The transmission characteristics of the EVF for displacement P [mm]
Figure 6. EVF step response with an open loop This paper discusses two strategies of the flow contro bulk materials. The first is the application ofa PID control of er, and the second is the use of a MPC controller. The design of the nonl open loop, PID controller was based nonlinear model o controller was based valid f the EVF. The design of the M on the step response of the PC on the linearized model of the EVF. The ity of the MPC controller was checked using inear model of t Simulink/Matlab, is shown in Fig.6 (A = 35%). he he EVF. The EVF step response with an which was obtained by simulation in
Figure 6. EVF step response with an open loop This paper discusses two strategies of the flow contro bulk materials. The first is the application ofa PID control of er, and the second is the use of a MPC controller. The design of the nonl open loop, PID controller was based nonlinear model o controller was based valid f the EVF. The design of the M on the step response of the PC on the linearized model of the EVF. The ity of the MPC controller was checked using inear model of t Simulink/Matlab, is shown in Fig.6 (A = 35%). he he EVF. The EVF step response with an which was obtained by simulation in
Figure 5. The transmission characteristics of the EVF for the material flow Qlg/sec] For the application of the MPC controller in the adopted model, it is necessary to select an EVF operating point in order to simplify the model and to present a simplified model in state space. The dependence of the bulk material flow rate with respect to the value of the parameter A[%] is shown in Fig.5. This figure was obtained using a simulation (f,,,.= 51.5 Hz).
Figure 5. The transmission characteristics of the EVF for the material flow Qlg/sec] For the application of the MPC controller in the adopted model, it is necessary to select an EVF operating point in order to simplify the model and to present a simplified model in state space. The dependence of the bulk material flow rate with respect to the value of the parameter A[%] is shown in Fig.5. This figure was obtained using a simulation (f,,,.= 51.5 Hz).
Figure 7. EVF output controlled by PI controller, ta47¢ =2 A closed-loop EVF was created using a PID controller block for two characteristic values of the T4779 parameter. The obtained simulation results are shown in Figures 7 and 8.
Figure 7. EVF output controlled by PI controller, ta47¢ =2 A closed-loop EVF was created using a PID controller block for two characteristic values of the T4779 parameter. The obtained simulation results are shown in Figures 7 and 8.
Figure 8. EVF output controlled by PI controller, tpi = 4 The value of the control signal is limited to 39% and the reference value of the output is set to 50 g/sec. In Figures we can see that it is possible to obtain a satisfactory step response of the system by a proper selection of the PID controller parameters. An increase in the value of the parameter t results in greater damping of its own oscillations. The MPC controller simulations were carried out in Simulink/Matlab using the "mpctool" function. Controller design description, identification and modelling studies are presented in the literature [13]. The transfer function in the state space is determined from equations (3) and (4). Input is a parameter A[%], and outputs are displacement (p) and flow rate (Q). In this paper, we examined two MPC controllers that differ in the number of controlled outputs. In the first case, only the value of the bulk material flow ( Q[kg/sec] ) was observed. In the second case, two outputs, the bulk material flow (Q[kg/sec] and displacement (p[m]), were observed. Constraints used in the simulations are the next: Ne A%1< 290 Ne nimm1l<795 N= Ooa/cecl < 58
Figure 8. EVF output controlled by PI controller, tpi = 4 The value of the control signal is limited to 39% and the reference value of the output is set to 50 g/sec. In Figures we can see that it is possible to obtain a satisfactory step response of the system by a proper selection of the PID controller parameters. An increase in the value of the parameter t results in greater damping of its own oscillations. The MPC controller simulations were carried out in Simulink/Matlab using the "mpctool" function. Controller design description, identification and modelling studies are presented in the literature [13]. The transfer function in the state space is determined from equations (3) and (4). Input is a parameter A[%], and outputs are displacement (p) and flow rate (Q). In this paper, we examined two MPC controllers that differ in the number of controlled outputs. In the first case, only the value of the bulk material flow ( Q[kg/sec] ) was observed. In the second case, two outputs, the bulk material flow (Q[kg/sec] and displacement (p[m]), were observed. Constraints used in the simulations are the next: Ne A%1< 290 Ne nimm1l<795 N= Ooa/cecl < 58
In order to verify the effectiveness of the proposed control algorithms, simulation experiments were performed on the EVF nonlinear model. Fig.9 shows the reference signal that was used in simulation without the influence of external disturbances on the monitored systems. For PID control, PI block ( t247;9 = 4 ) has been used. The resulting system response is shown in Figure 10. The EVF responses with the abovementioned MPC controllers for the reference signal shown in Fig.9 are shown in Figures 11 and 12. The results show that it is sufficient to observe only one output state in case of MPC controller. In this case, it is the bulk material flow rate Q. This fact simplifies the control algorithm, which is of particular importance to the practical implementation of MPCs.
In order to verify the effectiveness of the proposed control algorithms, simulation experiments were performed on the EVF nonlinear model. Fig.9 shows the reference signal that was used in simulation without the influence of external disturbances on the monitored systems. For PID control, PI block ( t247;9 = 4 ) has been used. The resulting system response is shown in Figure 10. The EVF responses with the abovementioned MPC controllers for the reference signal shown in Fig.9 are shown in Figures 11 and 12. The results show that it is sufficient to observe only one output state in case of MPC controller. In this case, it is the bulk material flow rate Q. This fact simplifies the control algorithm, which is of particular importance to the practical implementation of MPCs.
Figure 11. The EVF output controlled by MPC, Q[kg/sec] was observed. Figure 10. The EVF output controlled by PI controller, tp4779 =4
Figure 11. The EVF output controlled by MPC, Q[kg/sec] was observed. Figure 10. The EVF output controlled by PI controller, tp4779 =4
Figure 12. The EVF output controlled by MPC, O[kg/sec] and p[m] were observed.
Figure 12. The EVF output controlled by MPC, O[kg/sec] and p[m] were observed.
Figure 13. The changes of the material mass. results in Figures 11 and 12 show that the EVF is a robus system. Without external disturbances, the proposed contro algorithms do not improve the step response of the EVF. In order to test the proposed control algorithms, the system was exposed to disturbance in form of changes in the materia mass being transported. The material mass was increased by 7.5% in two seconds. The changes in material mass (Am) are shown in Fig.13. The response of the system without a closed loop is shown in Fig.14. The responses of PID and MPC controllers to this disturbance are shown in Figures 15 and 16, respectively. Fig.15 shows that the proposed methodology for the selection of parameters for the PID controller depends on the nature of the EVF. The controller keeps the set value of the flow of material, with acceptable deviations in steady state. Fig.16 shows that, compared to the PID controller, the MPC controller is significantly more sensitive to the observed disturbance. Given that the system was made to operate in a resonant mode, this behaviour of the MPC controller is expected. Changing the mass of the material causes a change in the EVF mechanical resonance. In this case, previously adopted model of the system is no longer adequate for the applied MPC controller.
Figure 13. The changes of the material mass. results in Figures 11 and 12 show that the EVF is a robus system. Without external disturbances, the proposed contro algorithms do not improve the step response of the EVF. In order to test the proposed control algorithms, the system was exposed to disturbance in form of changes in the materia mass being transported. The material mass was increased by 7.5% in two seconds. The changes in material mass (Am) are shown in Fig.13. The response of the system without a closed loop is shown in Fig.14. The responses of PID and MPC controllers to this disturbance are shown in Figures 15 and 16, respectively. Fig.15 shows that the proposed methodology for the selection of parameters for the PID controller depends on the nature of the EVF. The controller keeps the set value of the flow of material, with acceptable deviations in steady state. Fig.16 shows that, compared to the PID controller, the MPC controller is significantly more sensitive to the observed disturbance. Given that the system was made to operate in a resonant mode, this behaviour of the MPC controller is expected. Changing the mass of the material causes a change in the EVF mechanical resonance. In this case, previously adopted model of the system is no longer adequate for the applied MPC controller.
Figure 14. The response of the EVF without a closed loop.
Figure 14. The response of the EVF without a closed loop.
Figure 16. The response of the EVF with MPC controller. Figure 15. The response of the EVF with PID controller.
Figure 16. The response of the EVF with MPC controller. Figure 15. The response of the EVF with PID controller.
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