The interpretation of discontinuous state feedback control laws as nonanticipative control strategies in differential games

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A Universal Formula for Asymptotic Stabilization with Bounded Controls

Motivated by Artstein and Sontag universal formula, this brief paper presents an explicit proof of the universal formula for asymptotic stabilization and asymptotic disturbance rejection of a nonlinear system with mismatched uncertainties and time varying disturbances. We prove the stability via Lyapunov stability criteria. We also prove that the control law satisfies small control property such that the magnitude of the control signal can be bounded without the catastropic effect to the closed loop stability. For clarity, we benchmark the proposed approach with other method namely a Lyapunov redesign with nonlinear damping function. We give a numerical example to verify the results

Sliding Mode Controller Design Based on Pole Placement Method / Nor Laili Mahmud...[et al.]

Over the years, many researchers have considered the problem of stabilizing uncertain systems. In variable structure control (VSC) system, the controller structure around the plant is intentionally changed by using a viable high-speed switching feedback control to obtain a desired plant behavior or response. In this paper, the problem of designing a VSC law for uncertain system, Electrohydraulic control system is considered. Using Pole Placement approach, an alternative design method of a linear sliding surface which is linear to the state is developed. A sufficient condition for the existence of linear sliding surface is given and an explicit formula of linear sliding surfaces guaranteeing the quadratic stability of the reduced-order equivalent system dynamics restricted to the sliding surfaces is derived. The sliding mode controller is then applied to an Electrohydraulic servo system. The simulation works were performed using MATLAB/SIMULINK software. A comparison for the controller design using Pole Placement Method with and without the sliding mode control shows that the Pole Placement method with a sliding mode control method produces a better performance response

Sliding Mode Control Design for a Class of SISO Systems with Uncertain Sliding Surface

The problem of designing a sliding mode controller with uncertain sliding surface for a class of uncertain single-input-single-output systems is studied. The design case is handled by using the invariant transformation first in order to separate the sliding mode and the reaching mode of the sliding mode control system. It is shown that the sliding mode design needs not to consider the uncertainties of the sliding surface, which can be handled in the reaching phase design. The results generalize the robust design of the reaching phase such that one specific reaching phase design may agree with several sliding surfaces

Output feedback sliding mode control for time delay systems

This Thesis considers Sliding Mode Control (SMC) for linear systems subjected to uncertainties and delays using output feedback. Delay is a natural phenomenon in many practical systems, the effect of delay can be the potential cause -of performance deterioration or even instability. To achieve better control performance, SMC with output feedback is considered for its inherent robustness feature and practicality for implementation. In highlighting the main results, firstly a novel output feedback SMC design is presented which formulates the problem into Linear Matrix Inequalities (LMIs). The efficiency of the design is compared with the the existing literature in pole assignment. eigenstructure assignment and other LMI methods, which either require more constraints on system structures or are computationally less tractable. For systems with timevarying Slate delay, the method is extended to incorporate the delay effect in the controUer synthesis. Both sliding surface and controller design are formulated as LMI problems. For systems with input/output delays and disturbances. the robustness of SMC is degraded with arbitrarily small delay appearing in the high frequency switching component of the controller. To solve the problem singular perturbation method is used to achieve bounded performance which is proportional to the magnitudes of delay, disturbance and switching gain. The applied research has produced two practical implementation studies. Firstly it relates to the pointing control of an autonomous vehicle subjected to external disturbances and friction resulting from the motion of the vehicle crossing rough terrain. The second implementation concerns the attitude control of a flexible spacecraft with respect to roil, pitch and yaw attitude angles

Decentralized sliding mode control and estimation for large-scale systems

This thesis concerns the development of an approach of decentralised robust control and estimation for large scale systems (LSSs) using robust sliding mode control (SMC) and sliding mode observers (SMO) theory based on a linear matrix inequality (LMI) approach. A complete theory of decentralized first order sliding mode theory is developed. The main developments proposed in this thesis are: The novel development of an LMI approach to decentralized state feedback SMC. The proposed strategy has good ability in combination with other robust methods to fulfill specific performance and robustness requirements. The development of output based SMC for large scale systems (LSSs). Three types of novel decentralized output feedback SMC methods have been developed using LMI design tools. In contrast to more conventional approaches to SMC design the use of some complicated transformations have been obviated. A decentralized approach to SMO theory has been developed focused on the Walcott-Żak SMO combined with LMI tools. A derivation for bounds applicable to the estimation error for decentralized systems has been given that involves unknown subsystem interactions and modeling uncertainty. Strategies for both actuator and sensor fault estimation using decentralized SMO are discussed.The thesis also provides a case study of the SMC and SMO concepts applied to a non-linear annealing furnace system modelderived from a distributed parameter (partial differential equation) thermal system. The study commences with a lumped system decentralised representation of the furnace derived from the partial differential equations. The SMO and SMC methods derived in the thesis are applied to this lumped parameter furnace model. Results are given demonstrating the validity of the methods proposed and showing a good potential for a valuable practical implementation of fault tolerant control based on furnace temperature sensor faults

A Model-Free Control System Based on the Sliding Mode Control with Automatic Tuning Using as On-Line Parameter Estimation Approach

The sliding mode control algorithm and Lyapunov-based methods, have received much attention recently due to their ability to directly handle nonlinear systems while guaranteeing closed-loop tracking stability. In this work, a unique model-free sliding mode control technique has developed solely based on previous control inputs. The new method requires only knowledge of the system order and state measurements and does not require a theoretical model of the dynamic system. Lyapunov’s stability theorem is used in the controller formulation process to ensure closed-loop asymptotic stability. High frequency chattering of the control effort is reduced by using a smoothing boundary layer into the control law. Parameters variation during control operating and noise effect cannot be handled by the model-free controller if the controller tuning parameters are chosen arbitrarily since tracking performance becomes unacceptable. In addition, in previous work, the bounds of the input influence gain parameters were assumed to be known to derive the model-free controller. Therefore, in this work, a new approach is proposed for estimating the increment to the switching gain in real-time to ensure the sliding condition (which guarantees closed-loop tracking stability) is satisfied using a control law form that assumes a strictly unitary input influence gain. In formulation of estimation law, an exponential forgetting factor is combined with the least-squares estimator to ensure the updated data are used and past data are excluded. An automatic bounded forgetting tuning technique is developed to maintain the benefits of data forgetting while avoiding the possibility of gain unboundedness in absence of persistent excitation. The tuning estimator is assured that the resulting gain matrix is upper bounded regardless of the persistent excitation by suspending the data forgetting if the gain matrix reaches the specified upper bound. Simulations are performed on a series of linear and nonlinear SISO and MIMO systems with and without including actuator time-delay effects. Finally, a model is developed to simulate a quadcopter as a real-world application case. In all cases, the controller achieved perfect or near-perfect tracking performance using updated controller and on-line estimator tuning process