In this comparison aspect, the system responses under both controllers, as well as disturbance rejection, will be investigated. The system responses for the LE controller when the outer feedback gain is ( f 0.8) will be the basis for the comparison of closed loop performance.
Figure 6.1 shows the HVAC system responses under both controllers techniques when unity change is applied on the first input r t1( )representing the voltage on the inlet and exit motor fans, and with zero change at r t2( )and r t3( ).
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The Figure shows similar performance in both controllers in terms of very small steady state error for all the output responses and good transient responses but with exception of a significant overshoot for the volume airflow rate in the LE controller. Such overshoot will cause air noise for the blower for some time before it goes to lower steady state value, thus
reducing the air noise. Both controllers have demonstrated a high level of decoupling between the internal control loops. Considering the rise time definition, the LE controller is providing better performance over the DNA by producing faster responses as per the figure 6.1 and an important advantage against DAN controller.
Figure 6.2 shows the HVAC system responses under both controllers when unity change is applied on the second input r t representing the voltage on a chilled water pump, and with 2( ) zero change at r t1( )and r t .The volume air flow rate in the LE controller, is a also faster than 3( ) the same response in DNA controller. Moreover, the volume air flow rate response in DNA
Figure 6.1. System responses under both controllers techniques when unity change is applied on the representing the voltage on the inlet and exit motor fans, and with zero change at and .
% Output Change
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controller is taking longer time to reach its final steady state value. Both controllers show very small steady state error for all the output responses and demonstrate a high level of decoupling between the internal control loops.
Similarly, in Figure 6.3, the response of the temperature in the LE is faster than the DNA controller. In mean while the dynamic responses of the pressure and volume air flow rate in the LE are better than the same responses in the DNA.
The responses in the LE shows better performance than the performance in DNA in terms of system response speed, however, the comparison between both controllers in terms of disturbance rejection will also be investigated; it is an important aspect of comparison as HVAC systems are exposed to external disturbances very often.
Figure 6.2. System responses under both controllers techniques when unity change is applied on the representing the voltage on the chilled water pump, and with zero change at and .
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Time ( seconds) -0.4
-0.2 0 0.2 0.4 0.6 0.8 1
% Output Change
Pressure
Volume air flow rate Temperature Pressure Volime air flow rate Temperature
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Figure 6.4 shows the output responses at the disturbance unity step change 1( )t on the volume airflow output, while there is no disturbance change at the other outputs and no change at all reference inputs. The system performance under the DNA controller demonstrates better recovery response than the LE controller. Although the disturbance recovery is improving with the increased value of ( )f in LE control technique, it is failing to suppress the disturbance to low level in comparison with the DNA control technique. The output response when disturbance step change is applied on the air pressure output at the inlet of the ventilated volume and while there is no disturbance change at the other outputs and no change at the inputs is shown in Figure 6.5. In this case the recovery performance is quite well in both control techniques and suppressed the effect of the disturbance change accrued by signal making all the outputs values close to zero according to zero reference inputs values. However, the dynamics of the LE system responses in this case is better than the system responses dynamics of DNA controller.
)
2(t
)
2(t
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Figure 6.3. System responses under both controllers techniques when unity change is applied on the representing the abmient heat transfer, and with zero change at and .
% Output Change % Output Change
Figure 6.4. System responses following unity step change on the Pressure output, while there is no disturbance change at and and no change at all reference inputs , and
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% Output Change
Figure 6.5. System responses following unity step change on the Volume Air Flow Rate output, while there is no disturbance change at
and and no change at all reference inputs , and
Figure 6.6. System responses following unity step change on the Volume Air Flow Rate output, while there is no disturbance change at and
and no change at all reference inputs , and
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In Figure 6.6, the output responses when step disturbance change 3( )t is applied on the temperature output at the inlet of the ventilated volume and when there is no disturbance step change at the other outputs and no change at the inputs are shown.
The disturbance recovery performance can be considered as moderate in both control techniques where the influence of the disturbance by 3( )t is recovered for some of the system outputs to the value of 0.25 while remaining outputs to the zero values. However, the dynamic responses in the LE control technique are better than the dynamic responses in the DNA controller while recovering the influence of the disturbance3( )t
As an overview, the DNA control technique has showed capability to regulate the performance of the HVAC system, but the system outputs performance in the LE control technique is better than the responses performance of the DNA controller in terms of faster responses and better dynamics with the exception of the disturbance rejection on the pressure output in the LE, where the DNA reacted better than the LE in this case. The DNA control technique design is associated with a big number of decoupling first and second order compensators that makes the control solution complicated. The capability the DNA to regulate and to supress the disturbance effect would have not been achieved without decoupling the transfer function matrix with the big number of compensators. As a result, the LE controller provided good system performance and good disturbance rejection (apart from the disturbance rejection behaviour at the first output) by using simple passive gains and pre-compensators that are realistic, achievable and simple.