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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.
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with the global efforts to reduce the energy consumption inside the buildings and without sacrificing the indoor thermal comfort and air quality.
The control energy costs, under these conditions according to (Whalley and Ebrahimi, 2006), are proportional to
1800
2 2 2
1 2 3
0
( ) ( ) ( ) ( )
t
t
E t u t u t u t dt
, (6.1)where , , are the control output signals of each system control loop. Those are the voltages on the inlet and exit fans, the voltage on the chilled water pump and the ambient heat transferred into the ventilated volume
The Equation can be executed, simulated and run by Simulink software for 30 minutes for both controllers and with three different scenarios, a) when 1( )t is unity step change while the others disturbances are zero, b) when 2( )t is unity step change while the others disturbances are zero and c) when 3( )t is unity step change while the others disturbances are zero. The control structure selected for the LE controller in this comparison is when the outer loop gain is equal to 0.8
Figure 6.7 shows the amount the proportional control energy cost to run the HVAC plant under disturbance rejection scenarios in both controllers. The proportional control energy cost to recover the disturbance on the outputs of the system and to run the HVAC plant clearly lower in the LE is clearly than the DNA controller for three conditions. The big difference in the control energy dissipation for both controllers can be recognized from the difference in the control structure and procedure followed in each control technique. In the LE controller, simple passive gains and pre-compensators were used and calculated based on the optimization process, which calculate the gain values that makes the Performance Index representing the control energy Equation minimum and avoiding the utilization of integrators. However, the
)
1(t
u u2(t) u3(t)
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individual decoupled loops in the DNA required to have PID controllers have included integrators in order to get well-behaved system. The integrators in these controllers are responsible for the higher energy consumed.
Looking at Figure 6.7 the ratio of the proportional control energy cost in the LE to DNA controller at the time 900 seconds is 4.4
100, 39
100 and 22
100for Figures 6.7 a, 6.7 b and 6.7 c respectively, so that the added value of optimizing the control efforts of a specific control technique can be recognised from the above ratios.
As an overall comparison, both controllers have shown similar performance by showing capability to regulate the HVAC system outputs associated with good decoupling level and zero steady state error. On one hand the, the DNA was able to control the HVAC system in terms of, decoupling the internal loops, zero steady state values and disturbance rejection, but was associated with a high proportional control energy cost and complicated decoupling compensators. On the other hand, LE control technique has shown faster response and better system dynamics behaviour with simple passive forward and feedback gains avoiding employment integrators, but except for the behaviour on supressing the disturbance effect on the pressure output where the performance was moderate. Most important in the LE control technique is its performance in terms of least proportional control energy cost when recovering the disturbances and running the HVAC plant in comparison with DNA controller as per figures 6.7, which is the crucial aspect of judgment. It is important to mention that the LE controller can be an ideal control strategy solution that achieves least actuator activity, least heat and least wear and maintenance cost minimization without sacrificing the indoor thermal comfort and air quality.
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Figure 6.7. Proportional control energy cost, a: when diturbance is applied. b:
when diturbance is applied. c: when diturbance is applied, and with zero change at all reference inputs , and
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