Ahmad Jazlan

A frequency limited model reduction technique for linear discrete systems

This paper describes the model reduction framework for single-input single-output (SISO) discrete-time systems based on the preservation parameters such as Markov properties of the original system by applying a Frequency-Limited Impulse Response Gramian based Balanced Truncation method. This proposed method extends the Frequency-Limited Impulse Response Gramians model reduction method for continuous systems described in the recent paper in [20] to be applicable for discrete time systems. A numerical example is provided to compare the performances between various frequency limited model reduction methods at an arbitrarily selected frequency range within the passband of a digital filter. The stability of the reduced order models are also checked for each scenario.

Frequency interval balanced truncation of discrete-time bilinear systems

This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals of interest. In order to analyze the degree of controllability and observability of discrete-time bilinear systems with emphasis on particular frequency intervals of interest, new generalized frequency interval controllability and observability gramians are introduced in this paper. These gramians are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new generalized frequency interval controllability and observability gramians as part of the balanced truncation framework are provided to demonstrate the performance of the proposed method.

Indirect Vector Control of Induction Motor using Adaptive Sliding Mode Controller

This paper presents an implementation of Adaptive Sliding Mode Controller (ASMC) based robust speed control strategy for Indirect Vector Control (IVC) three phase Induction Motor (IM) drive. The software platform for modelling of IM in the synchronous rotating frame of reference for IVC is Matlab/Simulink. The primary focus of the proposed controller is to accomplish robustness for electrical faults perturbations, load disturbances, speed variation, and parameter uncertainties. The performance of the proposed control technique is compared with that of the conventionally tuned PI control scheme. The Simulation results of the ASMC guarantee effectiveness and robustness regarding overshoot, undershoot, rise time, fall time, and chattering for different operating conditions compared to the traditional PI control scheme.

Generalized gramian based frequency interval model reduction for unstable systems

Frequency interval controllability and observability gramian matrices are important in order to understand the characteristics of systems which are inherently frequency dependent. Obtaining these frequency interval controllability and observability gramian matrices requires solving a pair of Lyapunov equations. However for certain systems these Lyapunov equations are not solvable. In addition the eigenvalues of the product of the frequency interval controllability and observability gramians may also be complex numbers and therefore these gramians are not applicable to used in the context of model reduction. To overcome these issues, generalized frequency interval controllability and observability gramians are introduced in this paper and the applicability of these generalized gramians to be used in model reduction is demonstrated.

Time weighted model reduction of flat plate solar collectors

This paper presents the application of time weighted model reduction using cross gramians on a state space model derived from two partial differential equations representing the instantaneous thermal balance of a differential element of length along the absorber plate and the absorber plate to fluid heat convection process respectively of a flat plate solar collector. Finite difference method is applied onto both these partial differential equations where discretization in time and space is performed resulting in a high order linear discrete time invariant Single Input Single Output (SISO) state space model. Numerical results are provided to demonstrate and compare the performance of time weighted model reduction relative to balanced truncation.

A review on reduced order approximation for digital filters with complex coefficients using model reduction

This paper provides a review accompanied with examples regarding the usage of four basic discrete time model reduction techniques namely Balanced Truncation, Hankel Optimal Approximation, Impulse Response Gramians and Least Squares for the purpose of approximating an FIR digital filter with complex coefficients by its equivalent reduced order IIR digital filter. Simulation results indicate that stable reduced order IIR filters approximants with computational savings can be obtained using all the four techniques. However for a specified order, some model reduction techniques result in reduced order models which better approximate the original FIR digital filter compared to other techniques. The criteria used for comparison between the performances of the four model reduction algorithms were passband magnitude root mean squared error (RMSE) and computational cost. Two numerical examples are provided to demonstrate the application of model reduction techniques for complex co efficient filters and to compare the performances.