Ubaid M. Al-Saggaf

Stabilization of an inverted pendulum-cart system by fractional PI-state feedback

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=K(p)x(t)+K(I)I(α)(x(t)). The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n-1 (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments.

The q-Least Mean Squares algorithm

The Least Mean Square (LMS) algorithm inherits slow convergence due to its dependency on the eigenvalue spread of the input correlation matrix. In this work, we resolve this problem by developing a novel variant of the LMS algorithms based on the q-derivative concept. The q-gradient is an extension of the classical gradient vector based on the concept of Jackson?s derivative. Here, we propose to minimize the LMS cost function by employing the concept of q-derivative instead of the convent ional derivative. Thanks to the fact that the q-derivative takes larger steps in the search direction as it evaluates the secant of the cost function rather than the tangent (as in the case of a conventional derivative), we show that the q-derivative gives faster convergence for q 1 when compared to the conventional derivative. Then, we present a thorough investigation of the convergence behavior of the proposed q-LMS algorithm and carry out different analyses to assess its performance. Consequently, new explicit closed-form expressions for the mean-square-error (MSE) behavior are derived. Simulation results are presented to corroborate our theoretical findings. HighlightsDevelopment of the q-gradient.Development of the q-LMS algorithm.Derivation of closed-form expressions for the mean-square-error for the proposed algorithm.Extensive simulation results are carried out to corroborate the theoretical findings.

Closed-loop step response for tuning PID-fractional-order-filter controllers.

Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the fractional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled.

State feedback with fractional integral control design based on the Bode’s ideal transfer function

State feedback technique through a gain matrix has been a well-known method for pole assignment of a linear system. The technique could encounter a difficulty in eliminating the steady-state errors in some states. Introducing an integral element can effectively eliminate these errors. State feedback with fractional integral control is proposed, in this work, for pole placement of a linear time invariant system. The proposed method yields simple gain formulae. The paper presents the derivation of the design formulae. The method is applied to stabilise an inherently unstable inverted pendulum-cart system. Simulation and experimental results show the effectiveness of the proposed method for set-point tracking, disturbance rejection and stabilising the inverted pendulum. Comparison with the results obtained from applying Achermann’s formula is also presented.

Performance Analysis of Beamforming in MU-MIMO Systems for Rayleigh Fading Channels

This paper characterizes the performance metrics of MU-MIMO systems under Rayleigh fading channels in the presence of both cochannel interference and additive noise with unknown channel state information and known correlation matrices. In the first task, we derive analytical expressions for the cumulative distribution function of the instantaneous signal-to-interference-plus-noise ratio (SINR) for any deterministic beamvectors. As a second task, exact closed-form expressions are derived for the instantaneous capacity, the upper bound on ergodic capacity, and the Gram-Schmidt orthogonalization-based ergodic capacity for similar intra-cell correlation coefficients. Finally, we present the utility of several structured-diagonalization techniques, which can achieve the tractability for the approximate solution of ergodic capacity for both similar as well as different intra-cell correlation matrices. The novelty of this paper is to formulate the received SINR in terms of indefinite quadratic forms, which allows us to use complex residue theory to characterize the system behavior. The analytical expressions obtained closely match simulation results.

Fractional-order controller design for a heat flow process

In this paper, fractional-order controller designs for integer first-order plus time delay systems are investigated. Based on Bode’s ideal transfer function as a reference model, a new structure of the fractional-order controller is proposed. The internal model control principle is used to design the controllers. The effectiveness of the controllers is demonstrated through simulations and their efficiency is validated through experimentation on a heat flow platform.

Internal Model Control–Proportional Integral Derivative–Fractional-Order Filter Controllers Design for Unstable Delay Systems

An analytical design for proportional integral derivative (PID) controller cascaded with a fractional-order filter is proposed for first-order unstable processes with time delay. The design algorithm is based on the internal model control (IMC) paradigm. A two degrees-of-freedom (2DOF) control structure is used to improve the performance of the closed-loop system. In the 2DOF control structure, an integer order controller is used to stabilize the inner-loop, and a fractional-order controller for the stabilized system is employed to improve the performance of the closed-loop system. The Walton–Marshalls method, which is applicable to quasi-polynomials, is then used to establish the internal stability condition of the closed-loop system (the fractional part of the controller in particular) and to seek the set of stabilizing proportional (P) or proportional-derivative (PD) controller parameters.

Effects of Switching Network Topologies on Stealthy False Data Injection Attacks Against State Estimation in Power Networks

The stealthy attack, as a strategically designed false data injection attack against the power system state estimation mechanism, is able to let the corrupted measurements bypass residue-based bad data detectors with the same probability as that of uncorrupted measurements and is able to fool the system operator with the deviated estimates. While most of the existing articles assume the network topology to be fixed, the effects of switching topologies on such an attack are shown in this paper. A new mechanism is proposed to eliminate the possibility of such an attack via strategically shutting down some preselected transmission lines by turns and therefore switching the network topologies. The necessary and sufficient condition to achieve such elimination and the general form of possible attacks when the elimination is impossible are both formulated. The case where the attack is only stealthy in a subset of the preselected topologies is also studied. The general form of the possible estimate deviations caused by this “partially” stealthy attack is derived. Simulations and case studies are provided using different IEEE bus systems to show the efficiency of the proposed strategy, to discuss the countermeasures in the case when there always exist possible stealthy attacks, and to show how the possible deviations introduced by a “partially” stealthy attack could be affected by the decisions made by both the attacker and the system operator.

Family of state space least mean power of two-based algorithms

In this work, a novel family of state space adaptive algorithms is introduced. The proposed family of algorithms is derived based on stochastic gradient approach with a generalized least mean cost function J[k]=E[∥ε[k]∥2L] for any integer L. Since this generalized cost function is having power `2L’, it includes the whole family of the power of two-based algorithms by having different values of L. The novelty of the work resides in the fact that such a cost function has never been used in the framework of state space model. It is a well-known fact that the knowledge of state space model improves the estimation of state parameters of that system. Hence, by employing the state space model with a generalized cost function, we provide an efficient way to estimate the state parameters. The proposed family of algorithms inherit simplicity in its structure due to the use of stochastic gradient approach in contrast to the other model-based algorithms such as Kalman filter and its variants. This fact is supported by providing a comparison of the computational complexities of these algorithms. More specifically, the proposed family of algorithms has computational complexity far lesser than that of the Kalman filter. The stability of the proposed family of algorithms is analysed by providing the convergence analysis. Extensive simulations are presented to provide concrete justification and to compare the performances of the proposed family of algorithms with that of the Kalman filter.

Design of optimum error nonlinearity for channel estimation in the presence of class-A impulsive noise

In this work an optimum error nonlinearity is derived for the channel estimation in the existence of class-A impulsive noise. The main idea of the design is based on minimizing the steady-state error to reach the limit dictated by the Cramer-Rao Lower Bound (CRLB) of the implicit estimation process. By using the proposed method, optimum error nonlinearity is devised for long adaptive filters without employing any assumption on the distribution input regressor constituents and on the noise distribution, independence input regressor assumption and any kind of linearization. Moreover, to implement the proposed design, two different methods for estimating the variance of a priori estimation error are developed. Furthermore, an intelligent switching mechanism is also introduced to efficiently utilize the designed optimum error non-linearity for the impulsive noise. The theoretical results are testify through simulations, to show the superiority of the designed optimum error nonlinearity.