Extensive performance evaluation of the implemented model and controller reduction software has been performed, including three industrial examples: a linearized aircraft model, a CD-player finite element model and a gasifier model. These industrial examples are described in the following NICONET Report:
A.Varga. Model reduction routines for SLICOT, NICONET Report 1999-8, June 1999.
Linearized aircraft model of ATTAS.
This model describes the linearized rigid body dynamics of the DLR Advanced Technology Testing Aircraft System (ATTAS) during the landing approach. The nonlinear model of ATTAS used for linearization has been obtained using the object oriented modelling tool Dymola. Besides flight dynamics, this model includes actuators and sensors dynamics, as well as engine dynamics. Several low pass filters to eliminate structure induced dynamics in outputs are also included. The total order of the model is 55. The linearized model is non-minimal and has additionally an unstable spiral mode. Moreover, because of presence of position states, there are three pure integrators in the model and an additional one for the heading angle. Overall, there are 6 control inputs, 3 wind disturbance inputs, and 9 measurement outputs. This model serves basically for the evaluation of linear handling criteria in a multi-model based robust autopilot design.
Several low order models have been computed using the Balance & Truncate method. A 15-th order approximation has been computed which fits almost exactly the original 55 order model both in terms of step responses as well as of Nyquist frequency responses. Click here to see the good agreement obtained between the frequency responses of the original and reduced model for (2,2)-element of the corresponding transfer function matrix. Reduced models for longitudinal and lateral modes have been also computed. The reduced longitudinal ATTAS model has 7 states, 4 inputs and 4 outputs, while a reduced model for the lateral flight has 10 states, 2 inputs and 5 outputs.
CD-player finite element model
This is a 120-th order single-input single-output system which describes the dynamics between the lens actuator and radial arm position of a portable compact disc player. Due to physical constraints on the size of the systems's controller, a reduced model with order at most 15 is desired. Three 10-th order models have been determined using three methods available in SLICOT. Click here to see the performance of different computed approximations based on Bode plots. All methods approximate satisfactorily the central peak at frequency about 120Hz, but have different approximation properties at low and high frequencies. Both SPA and HNA approximations seems to be inappropriate, although the stationary error for the SPA method is zero. The B&T method appears to provide a good 10-th order approximation.
GEC ALSTHOM gasifier model.
A detailed nonlinear industrial gasifier model has been developed by GEC ALSTHOM, in October 1997, as a benchmark problem for simulation and robust control. The model includes all significant effects; e.g., drying of coal and limestone, pyrolysis and volatilisation of coal, the gasification process itself and elutriation of fines. This model has been validated using measured time histories from the British Coal CTDD experimental test facility and it was shown that the model predicts the main trends in fuel gas quality. Linearized models at 0%, 50% and 100% load are available to support a multi-model based robust controller design. The three linearized models have order 25 and are non-minimal. Numerical difficulties with respect to using these models have been reported. The apparent cause of difficulties is a poor scaling of the model.
The computed reduced order models of state dimension 16 cannot be practically distinguished from the original models on basis of time or frequency responses. No preliminary scaling of the original models was necesssary, since this feature is available by default in all SLICOT model reduction routines. Several lower order approximations of orders 6, 8 and 12 have been also computed. The 12th order models give very good approximations of the original models and can serve as bases for designing a unique robust controller ensuring satisfactory performance for all three models. A comparison on basis of the (3,5)-elements of the corresponding transfer-function matrices can be seen here.
In addition, extensive testing of the SLICOT model reduction software has been performed using several benchmark problems. The various examples for stable and unstable systems are described in chapter 4 of the NICONET Report No 1999-8: A. Varga "Model reduction routines for SLICOT", June 1999.