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Figure 11 Simulation results for (a) Position tracking with perturbation signal and (b) the error signal (see online version for colours)

Figure 11 Simulation results for (a) Position tracking with perturbation signal and (b) the error signal (see online version for colours)

Related Figures (13)

Figure 1 A complete system with an EPC, pneumatic actuator and a VGT (see online version for colours)
Figure 1 A complete system with an EPC, pneumatic actuator and a VGT (see online version for colours)
The total mass flow to the actuator is the difference of air mass flowing out from the actuator to reservoir and air mass flowing to the actuator from atmosphere. of the plunger position and their expression are given in the appendix. ®(p,.) i: a function which depends on the pressure ratio p, of the upstream pressure anc down stream pressure. Air mass flow is called choked flow when this ratio is <0.528 (See for example Heywood, 1988; Oosthuizen and Carscallen, 1997), air mass flow becomes constant at this point. Expression for ®(p,) is given in the following equation
The total mass flow to the actuator is the difference of air mass flowing out from the actuator to reservoir and air mass flowing to the actuator from atmosphere. of the plunger position and their expression are given in the appendix. ®(p,.) i: a function which depends on the pressure ratio p, of the upstream pressure anc down stream pressure. Air mass flow is called choked flow when this ratio is <0.528 (See for example Heywood, 1988; Oosthuizen and Carscallen, 1997), air mass flow becomes constant at this point. Expression for ®(p,) is given in the following equation
normal force and temperature variation. An adaptive LuGre model is shown in equation (13). where 0 represents variation in the model parameters. We obtained the adaptive friction model by considering that aerodynamic force is the variation in the LuGre model parameters.
normal force and temperature variation. An adaptive LuGre model is shown in equation (13). where 0 represents variation in the model parameters. We obtained the adaptive friction model by considering that aerodynamic force is the variation in the LuGre model parameters.
diaphragm position, diaphragm velocity, internal state of friction model, pressure in the actuator chamber and air mass flow from the pneumatic actuator, respectively. The nonlinear model develop in the previous section needs to be simplified for control purpose. We are proposing, herein, two different empirical methods to simplify our system, without causing significant change in the system response.
diaphragm position, diaphragm velocity, internal state of friction model, pressure in the actuator chamber and air mass flow from the pneumatic actuator, respectively. The nonlinear model develop in the previous section needs to be simplified for control purpose. We are proposing, herein, two different empirical methods to simplify our system, without causing significant change in the system response.
Figure 5 Cartography for mass flow as a function of plunger position and actuator pressure (see online version for colours)
Figure 5 Cartography for mass flow as a function of plunger position and actuator pressure (see online version for colours)
Figure 6 Cartography for mass flow as a function of applied signal and pressure difference (see online version for colours) Replacing this equation in the model we get the simplified model is shown in equation set (20). Where 21, v2, x3 and x4 are state variables for diaphragm position, diaphragm velocity, internal state of friction model and pressure inside the actuator chamber, respectively. It will be shown in the model validation section that simplified model does not increase significant modelling errors.
Figure 6 Cartography for mass flow as a function of applied signal and pressure difference (see online version for colours) Replacing this equation in the model we get the simplified model is shown in equation set (20). Where 21, v2, x3 and x4 are state variables for diaphragm position, diaphragm velocity, internal state of friction model and pressure inside the actuator chamber, respectively. It will be shown in the model validation section that simplified model does not increase significant modelling errors.
Figure 7 Test bench for the experimental tests (see online version for colours) The electro-pneumatic actuator models s have been simulated in matlab/simulink hown in equation set (16), (18) and (20) using the identified parameters given in the Table 1 for an industrial actuator. In the Figure 8 measured and simulation values of the actuator pressure and diap input 80%. Time response of the system hragm position are shown for duty cycle for the pressure fall is 0.3sec inside the actuator. All the three models follow dynamics of pressure with steady state error of +5 mbar. Diaphragm position for applied 0.35 sec. The maximum steady state error pressure is shown with time response of for all the simulation models is £0.3 mm. Tt can he ceen that agmnified emnirical modele are almnet ac arcirate ac The experiments were conducted on a the pneumatic valve and EPC used with the DV6TED4 commercial engine. Experimental results were obtained using the test bench shown in the Figure 7. National Instruments (NI) Compact RIO system was used for data acquisition. The test bench is equipped with two Druck pressure sensors with output from 20mA to 4mA. These sensors measure relative gauge pressure with range from 0 to —1bar. One sensor measures the actuator chamber pressure while the other measures source reservoir pressure. Position of the diaphragm is measured using a potentiometer mounted on the pneumatic actuator. Data is acquired using Compact-RIO modules (NI-9215) for analog input. EPC, Pierburg device, is energised with H-Bridge DC servo drive module (NI-9505). Sampling frequency for the CompactRio is fixed to 1 kHz.
Figure 7 Test bench for the experimental tests (see online version for colours) The electro-pneumatic actuator models s have been simulated in matlab/simulink hown in equation set (16), (18) and (20) using the identified parameters given in the Table 1 for an industrial actuator. In the Figure 8 measured and simulation values of the actuator pressure and diap input 80%. Time response of the system hragm position are shown for duty cycle for the pressure fall is 0.3sec inside the actuator. All the three models follow dynamics of pressure with steady state error of +5 mbar. Diaphragm position for applied 0.35 sec. The maximum steady state error pressure is shown with time response of for all the simulation models is £0.3 mm. Tt can he ceen that agmnified emnirical modele are almnet ac arcirate ac The experiments were conducted on a the pneumatic valve and EPC used with the DV6TED4 commercial engine. Experimental results were obtained using the test bench shown in the Figure 7. National Instruments (NI) Compact RIO system was used for data acquisition. The test bench is equipped with two Druck pressure sensors with output from 20mA to 4mA. These sensors measure relative gauge pressure with range from 0 to —1bar. One sensor measures the actuator chamber pressure while the other measures source reservoir pressure. Position of the diaphragm is measured using a potentiometer mounted on the pneumatic actuator. Data is acquired using Compact-RIO modules (NI-9215) for analog input. EPC, Pierburg device, is energised with H-Bridge DC servo drive module (NI-9505). Sampling frequency for the CompactRio is fixed to 1 kHz.
Figure 8 Validation of three proposed models for actuator pressure and diaphragm position, for 80% applied PWM signals (see online version for colours) The control objective: The control objective is to force the actuator to follow reference position trajectory in a robust manner. We want to design a robust position controller for the problem under discussion. We will develop one by one both sliding mode and backstepping controls in this section.
Figure 8 Validation of three proposed models for actuator pressure and diaphragm position, for 80% applied PWM signals (see online version for colours) The control objective: The control objective is to force the actuator to follow reference position trajectory in a robust manner. We want to design a robust position controller for the problem under discussion. We will develop one by one both sliding mode and backstepping controls in this section.
‘igure 10 (a) Position tracking of a sinusoid with SMC and backstepping techniques and (b) error in the tracking (see online version for colours) The controllers that are designed in the previous section were tested in the real time on the test bench shown in Figure 7. The sliding mode controller is implemented with well known twisting algorithm. The tuning parameters for both the controllers are given in Table 1. Two desired trajectories are tested using both controllers and their response has been shown in Figures 9 and 10.
‘igure 10 (a) Position tracking of a sinusoid with SMC and backstepping techniques and (b) error in the tracking (see online version for colours) The controllers that are designed in the previous section were tested in the real time on the test bench shown in Figure 7. The sliding mode controller is implemented with well known twisting algorithm. The tuning parameters for both the controllers are given in Table 1. Two desired trajectories are tested using both controllers and their response has been shown in Figures 9 and 10.
Figure 9 shows the position tracking results for the given trajectory and position error for both SMC and backstepping techniques. These results prove accuracy and finite time convergence properties for both controllers. However, the error signal with the second order sliding mode controller converges more rapidly to zero than backstepping controller. Whereas, the results obtained with backstepping control are satisfactory. The time response achieved for a step with these controllers is about 0.4 sec, which is comparable with open loop time response of the actuator i.e., 0.32 sec obtained from experiments. In Figure 9, tracking of a step and slow ramp trajectory and the error between desired and actual position are shown for both the controllers.
Figure 9 shows the position tracking results for the given trajectory and position error for both SMC and backstepping techniques. These results prove accuracy and finite time convergence properties for both controllers. However, the error signal with the second order sliding mode controller converges more rapidly to zero than backstepping controller. Whereas, the results obtained with backstepping control are satisfactory. The time response achieved for a step with these controllers is about 0.4 sec, which is comparable with open loop time response of the actuator i.e., 0.32 sec obtained from experiments. In Figure 9, tracking of a step and slow ramp trajectory and the error between desired and actual position are shown for both the controllers.
Table 1 Parameters values for the Diaphragm Table 2 Parameters identified from experimental data for the Pneumatic actuator Study of the nonlinear control techniques
Table 1 Parameters values for the Diaphragm Table 2 Parameters identified from experimental data for the Pneumatic actuator Study of the nonlinear control techniques
Effective flow area between actuator chamber and source reservoir is identified a: function of plunger position
Effective flow area between actuator chamber and source reservoir is identified a: function of plunger position
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