Ahmadreza Argha

On LMI-based sliding mode control for uncertain discrete-time systems

Abstract In this paper, a new approach to design a robust discrete-time sliding mode control (DSMC) is proposed for uncertain discrete-time systems. To this end, an LMI approach is used to develop a new framework to design the sliding function which is linear to the state. Our proposed robust DSMC can be applied to unstable systems, and also there is no need to stabilize the underlying system first. It has been argued in the literature that for the systems involving balanced external disturbances, using switching component is not needed. In this paper, it is shown that with the assumption of smoothness of the external disturbances, a different form of switching element in the controller can outperform the so-called linear controller in terms of the thickness of the boundary layer around the sliding function and the ultimate bound on the system state. Also, this paper extends the idea of disturbance estimation to the uncertain discrete-time systems. The disturbance estimator is exploited in the controller design and the boundedness of the obtained closed-loop system is analyzed. Also, two novel forms of variable structure DSMC are suggested in this paper.

Discrete-time sliding mode control for networked systems with random communication delays

This paper aims to design a robust discrete-time sliding mode control (DSMC) for the uncertain discrete-time networked systems involving time-varying Communication delays. To this end, the so-called Bernoulli random binary distribution is utilized to model the random time-varying delays. Then, by exploiting a specific sliding surface, a discrete-time sliding mode controller is designed such that the derived closed-loop system state and sliding function remain bounded in the presence of uncertainties and exogenous disturbances. Since the system state and sliding function are involved time-varying delays, the notion of exponentially mean square stability will be used to guarantee the stability/boundedness of the derived closed-loop system. The proposed robust DSMC can also overcome the conservatism of the existing methods in the literature. An illustrative example is presented to show the effectiveness of the proposed approach.

Sliding mode stabilisation of networked systems with consecutive data packet dropouts using only accessible information

ABSTRACT This paper develops a novel stabilising sliding mode for systems involving uncertainties as well as measurement data packet dropouts. In contrast to the existing literature that designs the switching function by using unavailable system states, a novel linear sliding function is constructed by employing only the available communicated system states for the systems involving measurement packet losses. This also equips us with the possibility to build a novel switching component for discrete-time sliding mode control (DSMC) by using only available system states. Finally, using a numerical example, we evaluate the performance of the designed DSMC for networked systems.

A novel sliding mode controller for DC-DC boost converters under input/load variations

In this paper a simple sliding mode controller based on the averaging state space model is proposed for a DC-DC boost converter. It is demonstrated to be easily implemented and has time-variant sliding coefficients. The proposed controller can effectively regulate the output voltage by controlling the switch states (through the dynamic duty cycles) even when the input voltage, load or output command varies. Furthermore the controller is independent of the inductor current and the load, although the load value is needed when designing the sliding coefficients. The constant switching frequency is maintained thus simplifying the design procedure, enhancing the regulation properties and benefiting the filter design. The controller has good dynamic response, overshoot damping and robustness. Comparative simulations are carried in MATLAB/Simulink between the proposed approach and a widely used PID controller to verify the effectiveness and feasibility of the proposed method.

A new approach to applying discrete sliding mode control to 2D systems

Sliding mode control has been applied previously to a specific form of 2D systems (Roesser model). In this paper a new approach (1D vectorial form) is introduced for this problem. Using 1D form to represent 2D systems can be used as an alternative strategy to reduce the inherent complexity of 2D systems and their applications. Unlike Wave Advanced Model (WAM) form (proposed by Porter and Aravena), the suggested 1D vectorial form, in this paper, has invariable dimension and consequently can be converted to regular form for sliding mode control (SMC). In this paper, the first Fornasini and Marchesini (FM) model of 2D systems which is a second order recursive form is considered. Meantime, the suggested method can be simply deployed to other first or second order 2D models.

Iterative learning control for 2-D systems

In this paper, the application of iterative learning control (ILC) in two-dimensional systems is considered and a method of ILC for 2-D systems is introduced so that the output of the process follows a desired trajectory. In this method the input of process in each iteration is determined by an innovative method called two-dimensional method by means of the obtained error between the output of the process and the desired trajectory which was given in previous iteration and the ability of this new method is illustrated by computerized simulation and the obtained results are compared with the results of one-dimensional method which was adapted to a 2-D one. Also the convergence of these methods is considered.

Mixed H2/H∞-based actuator selection for uncertain polytopic systems with regional pole placement

ABSTRACT This paper is devoted to the problem of designing an and/or row-sparse static output feedback controller for continuous linear time-invariant systems with polytopic uncertainty. The immediate application of the proposed approach lies within the problem of the optimal selection of a subset of available actuators during the fault accommodation stage of a fault-tolerant control scheme. Incorporating an extra term for penalising the number of actuators into the optimisation objective function, we propose an explicit scheme and two iterative procedures according to the reweighted ℓ1 (REL1) and reweighted iterative support detection (RISD) algorithms for the purposes of identifying the favourable row-sparse feedback gains. Furthermore, this problem formulation allows us to incorporate additional constraints into the designing problem such as regional pole placement constraints which provide more control over the satisfactory transient behaviour and closed-loop pole locations. In this paper, we present two examples which demonstrate the remarkable performance and broad applicability of the proposed approaches.

Using Iterative Learning Control methods for 2-D systems

In this paper, we discuss the application of Iterative Learning Control (ILC) algorithm in two-dimensional problems. Especially, the Optimal ILC is considered. For this issue by using 1-D model of WAM (Wave Advanced Model), the 2-D model converts to 1-D model. To generate the control rule in every iteration, by using optimization methods, a cost function would be minimized to achieve the 1-D model of WAM, the convergence of this method also will be checked. Besides the application of Iterative methods in continuous 2-D differential equations and nonlinear 2-D systems is examined in the current article.

Design of H2 (H∞)-based optimal structured and sparse static output feedback gains

Abstract This paper is devoted to the problem of designing an H 2 ( H ∞ )-based optimal sparse static output feedback (SOF) controller for continuous linear time invariant systems. Incorporating an extra term for penalising the number of non-zero entries of the static output (state) feedback gain into the optimisation objective function, we propose an explicit scheme and an iterative process in order to identify the desired sparse structure of the feedback gain. In doing so, the so-called reweighted l 1 -norm, which is known as a convex relaxation of the l 0 -norm, is exploited to make a convex problem through an iterative process rather than the original NP-hard problem. This paper will also show that this problem reformulation allows us to incorporate additional constraints, such as regional pole placement constraints which provide more control over the satisfactory transient behavior and closed-loop pole location, into the designing problem. Then using the obtained structural constraints, we solve the structural H 2 ( H ∞ ) SOF problem. Illustrative examples are presented to show the effectiveness of the proposed approaches.

Real-time modelling of heart rate response during exercise using a novel constrained parameter estimation method

This paper is devoted to the problem of real-time heart rate (HR) response modelling during treadmill exercise. A novel recursive constrained parameter estimation method is developed which in contrast to the conventional parameter estimation schemes (e.g. recursive least squares (RLS) method) can avoid the occurrence of the so-called blowup phenomena. By incorporation of a weighting upon 1) parameter variation relative to a priori HR response knowledge, 2) one-step parameter variation, into the objective function, an estimation scheme is obtained that in the absence of exciting data can avoid blowup. The proposed estimation scheme were experimentally verified using eight healthy male subjects and the results demonstrated that the designed scheme is able to identify the HR response of the exercising subjects in a real-time manner. As HR response is naturally a time-varying dynamics, the proposed online modelling method is of importance for the HR regulation during exercises, using a feedback controller with a desirable level of performance.