Discrete‐Time Sliding Mode Control with Outputs of Relative Degree More than One

This work deals with sliding mode control of discrete‐time systems where the outputs are defined or chosen to be of relative degrees more than one. The analysis brings forward important advancements in the direction of discrete‐time sliding mode control, such as improved robustness and performance of the system. It is proved that the ultimate band about the sliding surface could be greatly reduced by the choice of higher relative degree outputs, thus increasing the robustness of the system. Moreover, finite‐time stability in absence of uncertainties is proved for such a choice of higher relative degree output. In presence of uncertainties, the system states become finite time ultimately bounded in nature. The work presents in some detail the case with relative degree two outputs, deducing switching and non‐switching reaching laws for the same, while for arbitrary relative degree outputs, it shows a general formalisation of a control structure specific for a certain type of linear systems

Frequency-shaped and observer-based discrete-time sliding mode control

It is well established that the sliding mode control strategy provides an effective and robust method of controlling the deterministic system due to its well-known invariance property to a class of bounded disturbance and parameter variations. Advances in microcomputer technologies have made digital control increasingly popular among the researchers worldwide. And that led to the study of discrete-time sliding mode control design and its implementation. This brief presents, a method for multi-rate frequency shaped sliding mode controller design based on switching and non-switching type of reaching law. In this approach, the frequency dependent compensator dynamics are introduced through a frequency-shaped sliding surface by assigning frequency dependent weighing matrices in a linear quadratic regulator (LQR) design procedure. In this way, the undesired high frequency dynamics or certain frequency disturbance can be eliminated. The states are implicitly obtained by measuring the output at a faster rate than the control. It is also known that the vibration control of smart structure is a challenging problem as it has several vibratory modes. So, the frequency shaping approach is used to suppress the frequency dynamics excited during sliding mode in smart structure. The frequency content of the optimal sliding mode is shaped by using a frequency dependent compensator, such that a higher gain can be obtained at the resonance frequencies. The brief discusses the design methods of the controllers based on the proposed approach for the vibration suppression of the intelligent structure. The brief also presents a design of discrete-time reduced order observer using the duality to discrete-time sliding surface design. First, the duality between the coefficients of the discrete-time reduced order observer and the sliding surface design is established and then, the design method for the observer using Riccati equation is explained. Using the proposed method, the observer for the Power System Stabilizer (PSS) for Single Machine Infinite Bus (SMIB) system is designed and the simulation is carried out using the observed states. The discrete-time sliding mode controller based on the proposed reduced order observer design method is also obtained for a laboratory experimental servo system and verified with the experimental results

Stabilization and control of fractional order systems: a sliding mode approach

In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis.This monograph is based on the authors' work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fash

Improved model of Advanced Heavy Water Reactor(AHWR)for Control studies

This paper presents a modified version of coupled neutronics - thermal hydraulics model of Advanced Heavy Water Reactor (AHWR) for control studies. Earlier reported models assume, for the sake of simplicity, that the steam drum level and pressure are being strictly regulated at their respective set points, thereby neglecting these dynamics. However, such models are not suitable for analysis / controller design for the normal mode (load following mode) of operation of AHWR wherein the demand power setpoint is adjusted with respect to fluctuations in steam pressure. The work reported in this paper bridges this gap by including the steam drum pressure and level dynamics in the model. This leads to a model suitable for investigating control related aspects of all operational modes of the reactor. Efficacy of the proposed model is demonstrated through nonlinear simulations

A nonlinear sliding surface to improve performance of a discrete-time input-delay system

A sliding mode controller is proposed for an uncertain input-delay system to enhance performance. A nonlinear sliding surface is proposed to achieve better transient response for general uncertain discrete SISO linear systems with input delay. Both matched and unmatched perturbations are considered and ultimate boundedness of motion is proved. The step tracking problem is analysed. The proposed surface increases the damping ratio of the transformed system (delay free) as the output moves nearer to the setpoint. To simplify the surface design, a linear matrix inequality based tuning procedure is proposed. The control law is designed based on an equivalent control approach which guarantees one step reaching. The scheme is able to achieve low overshoot and low settling time simultaneously which is not possible with a linear sliding surface. Simulation results verify the effectiveness of the proposed nonlinear surface over different linear surfaces

Event-triggered discrete-time sliding mode control for high-order systems via reduced-order model approach

We propose the design of event-triggered (ET) discrete-time sliding mode (DTSM) control for a high-order discrete-time system via a reduced-order model-based approach. This design includes a triggering mechanism using a reduced-order state vector and a controller based on the modified Bartoszewicz' reaching law for a reduced-order model of the system, to stabilize the uncertain high-order system. The main advantages of using a reduced-order vector in the event condition are the low-order synthesis of the controller and the sampling pattern, which may be sparser than the full vector-based design. This motivation arises from the fact that relaxing a few components of the state vector in the triggering mechanism may decrease its rate of violation. An added advantage of the proposal is that the transmission of the reduced-order vector, particularly in a network-based implementation, can outperform the full-order based design due to the severe challenges that exist in the data network. The robust performance for the closed-loop system is achieved using the DTSM control. We show that our proposal guarantees the stability of the full-order plant with the reduced-order triggering mechanism. The control execution is Zeno-free because of the inherent discrete nature of the control. The efficiency of the proposed method is shown using the simulation results of a numerical example