Minimal unknown-input functional observers for multi-input multi-output LTI systems

Designing minimum possible order (minimal) disturbance-decoupled proper functional observers for multi-input multi-output (MIMO) linear time-invariant (LTI) systems is studied. It is not necessary that a minimum-order unknown-input functional observer (UIFO) exists in our proposed design procedure. If the minimum-order observer cannot be attained, the observer's order is increased sequentially through a recursive algorithm, so that the minimal order UIFO can be obtained. To the best of our knowledge, this is the first time that this specific problem is addressed. It is assumed that the system is unknown-input functional detectable, which is the least requirement for the existence of a stable UIFO. This condition also is a certificate for the convergence of our observer's order-increase algorithm. Two methodologies are demonstrated to solve the observer design equations. The second presented scheme, is a new design method that based on our observations has a better numerical performance than the first conventional one. Numerical examples and simulation results in the MATLAB/Simulink environment describe the overall observer design procedure, and highlight the efficacy of our new methodology to solve the observer equations in comparison to the conventional one.

On unknown-input functional observability of linear systems

Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability is introduced,and it is used as a certificate of the convergence of our algorithm. The proposed procedure looks for a number of additional auxiliary functions to be augmented to the original functions desired for reconstruction. The resulting UIFO is proper, and minimal (of minimum possible order). Moreover, the algorithm does not need the system to be unknown-input observable. A numerical example shows the procedure as well as the effectiveness of the proposed algorithm.

Improved manufacturing quality and bonding of laser machined microfluidic systems

Laser micro-machining offers a versatile tool for the rapid manufacturing of polymeric microfluidics systems, with a typical turn-around-time in the order of minutes. However, the chaotic nature of the thermal evaporative ablation process can yield a significant number of defects in the surface of the manufactured microchannels, in the form of residual condensed material. In this work we have investigated the use of solvent evaporation by which to not only laminate bond the laser machined structures but to remove a significant number of the defect formed by the condensation of residual polymer. Results are presented of the surface profiling of the bonded channel structures and demonstrations of the bonding of the microchips to produce autonomous capillary microchannels.

Functional observer design with application to pre-compensated multi-variable systems

Partial state estimation of dynamical systems provides significant advantages in practical applications. Likewise, pre-compensator design for multi variable systems invokes considerable increase in the order of the original system. Hence, applying functional observer to pre-compensated systems can result in lower computational costs and more practicability in some applications such as fault diagnosis and output feedback control of these systems. In this note, functional observer design is investigated for pre-compensated systems. A lower order pre-compensator is designed based on a H2 norm optimization that is designed as the solution of a set of linear matrix inequalities (LMIs). Next, a minimum order functional observer is designed for the pre-compensated system. An LTI model of an irreversible chemical reactor is used to demonstrate our design algorithm, and to highlight the benefits of the proposed schemes.

Minimal multi-functional observers for linear systems using a direct approach

The direct approach in designing functional observers was first presented in [1] for estimating a single function of the states of a Linear Time-Invariant (LTI) system. One of the benefits of the direct scheme is that it does not require solving the interconnected Sylvester equations that appear in the other observer design approaches. In the present paper, the direct approach is extended to reconstruct multiple functions of the states in such a way that the minimum possible order of the observer is achieved. The observer is designed so that an asymptotic functional observer can be obtained with arbitrary convergence rate. In the proposed methodology, it is not necessary that a reduced order observer exists for the desired functions to be estimated. To release this limitation, an algorithm is employed to find some auxiliary functions in the minimum required number to be appended to the desired functions. This method assumes that the system is functional observable. This assumption however is less restrictive than the observability and detectability conditions of the system. A numerical example and simulation results explain the efficacy and the benefits of the proposed algorithm.

Nonlinear controller design for vehicle-to-grid systems with output LCL filters

This paper presents a nonlinear controller design for vehicle-to-grid (V2G) systems with LCL output filters. The V2G systems are modeled with LCL output filters in order to eliminate harmonics for improving power qualities and the nonlinear controller is designed based on the feedback linearization. The feasibility of using the appropriate feedback linearization approaches, either partial or exact, is also investigated through the feedback linearizability of V2G systems. In this paper, partial feedback linearization is used to design the controller with a capability of sharing both active and reactive power in V2G systems. The performance of the proposed controller controller is evaluated on a single-phase full-bridge converter-based V2G system with an LCL output filter and compared to that of without any filter. Simulation results clearly demonstrate the harmonic elimination capabilities of the proposed V2G structure with the proposed control scheme.