Phase and Gain Margins with Third Order Sliding Mode Control: An Integrated Guidance Application

The objective of this paper is to design a nonlinear second order sliding mode control for stabilizing the power angle of synchronous generator modeled by a standard third order model. The Standard Sliding Mode (SSM) controller produces oscillations (or “chattering”) in the closed-loop system. The new approach High Order Sliding Mode (HOSM) is proposed to reduce this phenomenon. The designed controller is smooth and robust with respect to different transient faults and enables to compensate the inherent nonlinearities of the generator. The responses of the system with the proposed controller are compared with those obtained with some other kinds of power stabilizers when the system is subjected to a variety of disturbances. Simulations on a single-machine in bus power system have demonstrated better performances compared with existing controllers. They show that the power system can keep transiently stable and achieve voltage regulation indirectly.

The main purpose of this paper is to design a robust second order sliding mode controller that can deal with uncertain nonlinear systems. This controller can keep the main advantages of the first order sliding mode controller, such as the ability to make the system asymptotically stable by forcing the error and its derivatives to have a zero value, the simplicity in the operation, and the robustness in the existence of perturbations. In spite of the features that characterize the first order sliding mode controller (1 SMC), it still suffers from the unwanted phenomenon “chattering”, which originates from a discontinuous control part (sign function). In this context, saturation function can be used instead of sign function to reduce this problematic chattering. Different from the saturation function method, the second order sliding mode controller can be used to overcome the chattering; suffered by the first order sliding mode controller and to retain the stability and performance of the system. In this paper, the twisting and the super twisting second-order algorithms of the sliding mode controller were used, and their results were compared with the first order sliding mode controller. So, this subject focused on the chattering problem who suffers from it the 1 SMC and try to reduce it by using the 2 SMC, the uncertain pendulum system was adopted in this work for the purpose of checking the three controllers. The simulations results showed that the second order sliding mode controller has the ability to reduce both the chattering magnitude and the steady state error and achieve an asymptotically stable system. The results were obtained by using MATLAB programming.

The paper proposes an approach to second order sliding mode control for multi-input multi-output (MIMO) nonlinear uncertain systems. Second order sliding mode techniques for single-input single-output (SISO) systems show, with respect to standard sliding mode control, the same properties of robustness and precision, feature a higher order accuracy and can be exploited to eliminate the chattering effect. The application of second order sliding mode control to MIMO nonlinear systems is a challenging matter. The presented MIMO control method applies to a quite large class of nonlinear processes affected by uncertainties of general nature; the control design is simple; the conditions of existence on the controllers are weak. The proposed procedure represents a general approach to the second order sliding mode control of MIMO systems

Heavy disturbances caused mainly by wind and friction in the mount drive system greatly impair the pointing accuracy of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). To overcome this negative effect, a third order Higher Order Sliding Mode (HOSM) controller is proposed. The key part of this approach is to design an appropriate observer which obtains the acceleration state. A nonlinear adaptive observer is proposed in which a novel polynomial model is applied to estimate the internal disturbances of the mount drive system. Theoretical analysis demonstrates the stability of the proposed observer. Simulation results show that this nonlinear adaptive observer can obtain a high precision acceleration signal which completes the HOSM controller. Furthermore, the HOSM approach can easily satisfy the position tracking requirements of the LAMOST mount drive system.

Second order sliding mode controllers for altitude control of a quadrotor UAS: Real-time implementation in outdoor environments

This paper focuses on maintaining the liquid level in tank two in the coupled tank control system with the help of the sliding mode control (SMC). SMC is the potent controller for coupled tank liquid level system under tracking conditions. Sliding mode controller (SMC) is nonlinear control it applies a discontinuous control signal. The main advantages of sliding mode are low sensitivity to plant parameter variations and disturbances. To maintain desired liquid levels in a nonlinear coupled tank is a great challenging task so this problem better handled by SMC. To control this liquid level process a SMC strategy is used we have first order SMC and second order SMC. Regulating this system in less time with proper control signal is not possible in first order SMC due to chattering is obtained which yields unwanted control signal. To fill tank-2 in less time with smooth control signal is possible in higher order SMC. Next, second order SMC is applied and stability is reached fast and no chattering phenomenon. These can be shown in the simulation results with the help of MATLAB. This application report describes how to develop SMC for liquid level control in coupled tank system.

This chapter deals with the tracking problem of robot manipulators. These systems are described by highly nonlinear and coupled equations. Higher order sliding mode controllers are then proposed to ensure stability and robustness of uncertain robot manipulators. The motivation for using high order sliding mode mainly relies on its appreciable features, such as high precision and elimination of chattering in addition that ensures the same performance of conventional sliding mode like robustness. In this chapter we propose two high order sliding mode controllers. The first guarantees a continuous control eliminating the chattering phenomenon. Instead of a regular control input, the derivative of the control input is used in the proposed control law. The discontinuity in the controller is made to act on the time derivative of the control input. The actual control signal obtained by integrating the derivative control signal is smooth and chattering free. The second controller is an adaptive version of high order sliding mode controller. The goal is to obtain a robust high order sliding mode adaptive gain control law to respect to uncertainties and perturbations without the knowledge of uncertainties/perturbations bound. The proposed controller ensures robustness, precision and smoothness of the control signal. The stability and the robustness of the proposed controllers can be easily verified by using the classical Lyapunov criterion. The proposed controllers are tested to a three-degree-of-freedom robot to prove their effectiveness.

This paper deals with the design of a third order Sliding Mode Control (SMC) algorithm for a perturbed chain of integrators with box constraints on state variables. The proposed strategy takes into account a robust generalization of the so-called Fuller's Problem, which is a standard optimal control problem for a chain of integrators under critical uncertainty condition, and proves to steer the system trajectories to the origin of the state space in finite time, while satisfying the imposed constraints. The proposed algorithm is tested in simulation to solve a trajectory-tracking problem for a nonholonomic car.

Electrical marine propulsion systems are characterized by very high level requirements in terms of compactness, acoustic behavior and reliability. In this particular context, the use of multiphase PM machines associated with VSI drives appears to be a very efficient solution. Presented work focus on the use of such a system in open circuited phase fault conditions. With this kind of system it is possible to determine optimal current references which maximize the torque density of the system when one or two phases are open circuited. Classical linear controllers (as PID for example) cannot provide a correct tracking of these optimal current references because they have a highly dynamical behavior. We propose in this paper to combine this optimal current reference generation with High Order Sliding Mode (HOSM) control. This kind of solution allows a good tracking of these unconventional current references with a fixed switching frequency for the VSI. This method is validated experimentally using a low power experimental set-up which associates a 5-phase PM machine with a DSP controlled IGBT 5-leg VSI drive.

In this paper combination of standard and second order sliding mode controller are used and investigated for congestion control problem of differentiated Services (Diff-Serv) networks. Robustness against modeling uncertainties and disturbances are major features of sliding mode controller. Chattering phenomenon affects sliding mode congestion control; to overcome this problem, second order sliding mode control (SOSMC) is proposed as a congestion controller but this controller has slower response to SMC. Combination SMC and SOSMC gives better response. There are three types of traffics in Diff-Serv networks; i.e. three types of queues and based on that, the quality of their services are categorized. Each of these types of traffic has its own congestion control mechanisms. Stability of each controller is proved by Lyapunov stability law. To evaluate the capabilities of our proposed robust control strategy, simulation results are provided for both sliding mode controllers and second order slide mode controllers and their corresponding efficiencies are compared.

The success of the sliding mode control (SMC) is due to the simplicity of its implementation and its robustness against external disturbances via state space and input output model. In spite of this characteristic, the sliding mode control (SMC) suffers from a main drawback known as the ‘chattering phenomenon’. In order to overcome this problem, a new discrete second order sliding mode control via input output model is proposed in this paper. A stability analysis of the proposed control was then studied. To illustrate the effectiveness of the proposed discrete second order sliding mode control law, a classical discrete sliding mode control and discrete second order sliding mode control were applied to a real discrete second order system via input output model. The experimental results of the proposed discrete sliding mode control law show good performances in terms of the rejection of the external disturbances and the reduction of the chattering phenomenon.

This work presents a nested super-twisting second-order sliding mode speed controller for a brushless direct current motor with a high order sliding mode observer used for back electromotive force (back-EMF) estimation. Due to the trapezoidal nature of the back-EMF, a modified Park transformation is used in order to achieve proper field orientation. Such transformation requires information from the back-EMF that is not accessible. A second-order sliding mode observer is used to estimate the back electromotive forces needed in the modified transformation. Sliding mode control is known to be robust to matched uncertain disturbances and parametric variations but it is prone to unmatched perturbations that affect the performance of the system. A nested scheme is used to improve the response of the controller in presence of unmatched disturbances. Simulations performed under similar conditions to real-time experimentation show a good regulation of the rotor speed in terms of transient and steady-state responses along with a reduced torque ripple.

The integration of renewable energy sources (RESs) at the edge of the grid plays a contributory role in advancing the transition to a sustainable energy future. However, this transition introduces significant variability, which challenges the maintenance of frequency stability in power systems. To address the impacts of RES variability, various robust control strategies have been developed. This paper compares the performance of different advanced sliding mode control (SMC) approaches, i.e., super twisting (ST) algorithm‐based second order sliding mode control (STSOSMC), second order sliding mode control (SOSMC), double integral sliding mode control (DISMC) and integral sliding mode control (ISMC) with conventional sliding mode control (SMC) for load frequency control with stochastic RESs such as biogas generators (BG) and wind‐based doubly fed induction generators (DFIG). The impact of the advanced sliding mode controllers on the voltage and rotor angle stability of the system is also explored. The efficacy of the controllers is tested under different load disturbances, considering nonlinearities such as communication delay (CD), sensor inaccuracy (SI), governor dead band (GDB), and generation rate constraint (GRC). The results demonstrate that STSOSMC achieves superior frequency regulation with minimal chattering and outperforms other controllers in terms of settling time, overshooting, and undershooting in frequency deviation. The result also demonstrates the effectiveness of STSOSMC in managing the variability and disturbances of RESs. Therefore, it could be considered the most robust control mechanism from the edge of the grid system with high penetration of RESs.

A novel analogue circuit environment to implement higher order sliding mode (HOSM) and continuous finite time (CFT) stabilising controllers is proposed in this paper. The novelty lies in the ability of the circuit to capture the underlying theoretical features by producing non-Lipschtiz controller implementations. The circuit can be built using readily available off-the-shelf components. Since the environment is based on an analogue circuit, the development matches the mathematics of a class of non-Lipschitz differential equations more closely than its digital counterparts thereby narrowing the theory-practice gap. The key contribution is the implementation of a class of non-Lipschitz controllers using analogue components thereby nullifying steady-state tracking errors without the need for integral action, a key concept of both HOSM and CFT philosophies with the former being more robust. The circuit has plug-and-play functionality similar to the ubiquitous PID controllers, where recent results on the tuning of HOSM controller parameters give the potential to replicate the classical PID controller tuning approach. The functionality is demonstrated by the closed-loop speed control of a dc motor, although the results are applicable to other engineering problems which are also discussed.

In this paper we present a nonlinear control using super twisting high order sliding mode for a vertical axis wind turbine (VAWT) with direct attack based on doubly-fed induction generator (DFIG) supplied by an AC-AC converter. In the first place, we carried out briefly a study of modeling on the whole system (H-darrieus wind turbine). In order to control the power flowing between the stator of the DFIG and the grid, a proposed control design uses high order sliding mode technique is applied for implementing to remove completely the chattering phenomenon on a conventional sliding mode control. The use of this method provides very satisfactory performance for the DFIG control, and the chattering effect is also reduced by this technique. The machine is tested in association with a wind turbine. Simulations results are presented and discussed for the whole system.