A new result for balancing control of a bicycle robot (bicyrobo), employing reduced-order modelling of a pre-specified design controller structure in higher-order to derive into a reduced controller has been presented in this paper. The bicyrobo, which is an unstable system accompanying other causes of uncertainty such as UN-model dynamics, parameter deviations, and external disruptions has been of great interests to researchers. The controllers in the literature reviews come up with the higher order controller (HOC), the overall system becomes complex from the perspective of analysis, synthesis, enhancement and also not easy to handle it's hardware implementation. Therefore, a reduced-order pre-specified controller is developed in this work. It is effective enough to tackle unpredictable dynamics. The reduced-order controller (ROC) design is based on model order reduction (MOR) method, which is a resutl of hybridization of balanced truncation (BT) and singular perturbation approximation (SPA) approach. The reduced model so obtained, which retains DC gain as well, has been named as balanced singular perturbation approximation (BSPA) approach. It is based upon the preservation of dominant modes (i.e. appropriate states) of the system as well as the removal of states having relatively less important distinguishing features. The strong demerit of the BT method is that, for reduced-order model (ROM), steady-state values or DC gain do not match with the actual system values. The BSPA has been enabled to account for this demerit. The method incorporates greater dominant requirements and contributes to a better approximation as compared to the existing methods. The results obtained by applying proposed controller, are compared with those of the controllers previously designed and published for the same type of work. Comparatively, the proposed controller has been shown to have better performance as HOC. The performance of HOC and ROC is also examined with perturbed bicyrobo in terms of time-domain analysis and performance indices error.
Model Boundary Approximation Method as a Unifying Framework for Balanced Truncation and Singular Perturbation Approximation