HVAC multivariable system modelling and control

Abstract

Heating, Ventilation and Air Conditioning (HVAC) is a multivariable process where any alteration with one system input affects most or all of the system’s outputs simultaneously. Owing to its comprehensiveness, a readily derived multivariable HVAC mathematical model is selected for this work, mainly a hybrid distributed-lumped parameters model. As the transfer function matrix was not established in the selected HVAC model, it was exclusively developed in this study, using the time domain graphical responses of the chosen model. Based on the developed transfer function matrix, a conceptual two-step approach was followed to control HVAC model performance. The first was decoupling the interactions that affect all the system outputs, and the second was designing proper PID controllers for each decoupled loop similar to those used for single input single output (SISO) systems. A direct Nyquist Array (DNA) multivariable control strategy was used for this purpose and successfully decoupled the HVAC system into three separate (SISO) loops. Three PID controllers afterwards were applied for each decoupled loop. The results showed quite decoupled system outputs with a minor coupling percentage so that any change in a system input only affected the corresponding system output. The output responses are also underdamped with almost zero steady-state error confirming the effectiveness of the selected PID parameters. The values of steady-state responses are obtained in (10–15) s compared with (200–600) s of open-loop response time. However, various overshoot percentages in the responses are encountered but are relatively small, with a short settling time, so they don’t affect the thermal comfort of the ventilated volume. System stability using the Nyquist criterion has also been examined and found to satisfy the criterion. The multivariable DNA control technique and the SISO closed-loop PID controllers have shown the capability to suppress external disturbances and restore the system to its original functional steady-state values.

Study on Multivariable Dynamic Matrix Control for a Novel Solar Hybrid STIGT System

“…Staudt et al used MPC (Modelpredictive control) in heat pumping devices for wider operating ranges and better part load capability than the PID [17]. The DNA (Direct Nyquist Array) method investigated by Touqan et al suppressed disturbances in HVAC systems better than the PID [18]. The study conducted by Zhao et al showed that MLR (Multivariable linear regression) enhanced COP values and reduced electricity consumption over the PID [19].…”