{'fraction_non_alphanumeric': 0.020097020097020097, 'fraction_numerical': 0.0, 'mean_word_length': 4.511450381679389, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Stability analysis for a VAV test rig

A stability analysis for a simple VAV test rig is presented. The test rig is described by a series of non-linear mathematical models. For this system, the well-known stability analysis for linear systems cannot be applied directly. As a result, this paper presents two new approaches for the analysis of the closed-loop stability of the non-linear VAV test rig. The first approach is based on a non-linear empirical model simulation. In this approach, different operating points of the supply fan PI control are applied and the stable regions of the model are obtained and compared with the results from experiments. The boundary lines of the stability region are given in terms of the proportional gain k p and the integral gain k i of the PI controller. The results are reasonably accurate. The second approach uses a linearised model with Lyapunov's method for non-linear systems, and the stability is analysed at selected fan operating points. Again, a stability region is obtained in terms of k p and k i. This region can be used for the selection of stable control and can help in commissioning. Although the linear model with Lyapunov's method gives results that are less accurate than those of the non-linear model, the former is more flexible and quicker in use, despite being more complex in derivation. Further refinement of the linear model in the future may well yield more accurate results.