Abstract
In this paper we present a case study involving mathematical modeling, system identification, and controller design of a two tank fluid level system. The case study is motivated by a realistic application of a two tank problem. We address some fundamental control oriented issues such as physical plant design and identification, transformation from discrete-time to continuous-time, and finally the controller design. We also introduce a novel physical system identification algorithm consisting of subspace identification, followed by a similarity transformation computation to extract the physical parameters of the system. The controller design is done by Pole Placement.

Abstract
The problem of estimating the motion and orientation parameters of a rigid object from two m - D point set patterns is of significant importance in medical imaging, electrocardiogram (ECG) alignment, and fingerprint matching. The rigid parameters can be defined by an m x m rotation matrix, a diagonal m x m scale matrix, and an m x 1 translation vector. All together, the total number of parameters to be found is m(m + 2). Several least squares based algorithms have recently appeared in the literature. These algorithms are all based on a singular value decomposition (SVD) of the m x m cross-covariance matrix between the two data sets. However, there are cases where the SVD based algorithms return a reflection matrix rather than a rotation matrix. Some authors have introduced a simple correction for guarding against such cases. Other types of algorithm are based on unit quaternions which guarantee obtaining a true rotation matrix. In this paper we introduce a principal component based registration algorithm which is solved in closed-form. By using matrix vectorization properties the problem can be cast as one of finding a rank-1 symmetric projection matrix. This is equivalent to solving a Sylvester equation with equality constraints. Once the solution is obtained, we apply the inverse vectorization operation to estimate the rotation and scale matrices, along with the translation vector. We apply the proposed algorithm to the alignment of ECG signals and compare the results to those obtained by the SVD and quaternion based algorithms.

Abstract
In this paper we introduce an identification algorithm for MIMO bilinear systems subject to deterministic inputs. The new algorithm is based on an expanding dimensions concept, leading to a rectangular, dimension varying, linear system. In this framework the observability, controllability, and Markov parameters are similar to those of a time-varying system. The fact that the system is time invariant, leads to an equaivaleet linear deterministic subspace algorithm. Provided a rank condition is satisfied, the algorithm will produce unbiased parameter estimates. This rank condition can be guaranteed to hold if the ratio of the number of outputs to the number of inputs is larger than the system order. This is due to the typical exponential blow-out in the dimensions of the Hankel data matrices of bilinear systems, in particular for deterministic inputs since part of the input subspace cannot be projected out. Other algorithms in the literature, based on Walsh functions, require that the number of outputs is at least equal to the system order. For ease of notation and clarification, the algorithm is presented as an intersection based subspace algorithm. Numerical results show that the algorithm reproduces the system parameters very well, provided the rank condition is satisfied. When the rank condition is not satisfied, the algorithm will return biased parameter estimates, which is a typical bottleneck of bilinear system identification algorithms for deterministic inputs. © 2005 IEEE.

Abstract
In this paper the Wiener-Hammerstein Benchmark is identified as a bilinear discrete system. The bilinear approximation relies on both facts that the Wiener-Hammerstein system can be described by a Volterra series which can be approximated by bilinear systems. The identification is performed with an iterative bilinear subspace identification algorithm previously proposed by the authors. In order to increase accuracy, polynomial static nonlinearities were added to the bilinear model input. These Hammerstein type bilinear models are then identified using the same iterative subspace identification algorithm.

Abstract
A new approach to gas leakage detection in high pressure distribution networks is proposed, where two leakage detectors are modelled as a linear parameter varying (LPV) system whose scheduling signals are, respectively, intake and offtake pressures. Running the two detectors simultaneously allows for leakage location. First, the pipeline is identified from operational data, supplied by REN-Gasodutos and using an LPV systems identification algorithm proposed in [1]. Each leakage detector uses two Kalman filters where the fault is viewed as an augmented state. The first filter estimates the flow using a calculated scheduling signal, assuming that there is no leakage. Therefore it works as a reference. The second one uses a measured scheduling signal and the augmented state is compared with the reference value. Whenever there is a significant difference, a leakage is detected. The effectiveness of this method is illustrated with an example where a mixture of real and simulated data is used.

Abstract
In this paper the Wiener-Hammerstein system proposed as a benchmark for the SYSID 2009 benchmark session is identified as a bilinear discrete system. The bilinear approximation relies on both facts that the Wiener-Hammerstein system can be described by a Volterra series which can be approximated by bilinear systems. The identification is performed with an iterative bilinear subspace identification algorithm previously proposed by the authors. In order to increase accuracy, polynomial static nonlinearities are added to the bilinear model input. These Hammerstein type bilinear models are then identified using the same iterative subspace identification algorithm. © 2009 IFAC.