Robust Exact Differentiator Research Articles

Application of Higher Order Sliding-Mode Concepts to a Throttle Actuator for Gasoline Engines

In this paper, the control of an electronic throttle valve based on second-order sliding-mode concepts is presented. The so-called twisting algorithm is chosen as the control law. It is shown that the tracking performance for discontinuous reference signals is significantly improved by introducing nonlinear damping by appropriately specifying the sliding surface. The control concept requires the measured plate angle as well as its time derivative, which is computed with the help of a robust exact differentiator. The effectiveness of the proposed concept, consisting of a twisting algorithm for control and supertwisting algorithm for differentiation, is demonstrated by experimental results.

Global Exact Tracking for Uncertain Systems Using Output-Feedback Sliding Mode Control

This note presents a solution to the problem of global exact output tracking for uncertain linear plants with arbitrary relative degree using output-feedback sliding mode control. The key idea to overcome the relative degree obstacle is to introduce a hybrid compensator by combining, through switching, a standard lead filter with a robust exact differentiator, based on higher-order sliding modes, achieving uniform global exponential practical stability and asymptotic exact tracking.

Homogeneous High-Order Sliding Modes

Homogeneity of dynamic systems provides for a number of practically important features. In particular, the finite-time convergence is easily proved, and the asymptotic accuracy is readily calculated in the presence of input noises, delays and discrete sampling. General uncertain single-input-single-output regulation problems are only solvable by means of discontinuous control via the so-called high-order sliding modes (HOSM). Robust output-feedback homogeneous HOSM controllers are produced, using robust exact homogeneous differentiators. The dangerous chattering effect is removed in a standard way. The system performance is not sensitive to the presence of unaccounted-for fast stable dynamics of actuators and sensors, delays and discrete sampling.

Quasi-continuous high-order sliding-mode controllers for reduced-order chaos synchronization

In this paper the problem of the reduced-order synchronization of systems of different order is considered. A control design based on robust exact differentiators and quasi-continuous high-order sliding mode-controllers is proposed ensuring the reduced-order synchronization in spite of master/slave mismatches. Simulation results are provided in order to illustrate the performance of the proposed synchronization scheme.

Higher Order SM Block Control of Nonlinear Systems with Unmodeled Actuators

In this paper, a control strategy is proposed for robust stabilization of nonlinear perturbed plants in the presence of actuator unmodeled dynamics. The block control technique is applied to design a nonlinear SM manifold for achieving the error tracking, and High Order Sliding Mode (HOSM) algorithm is implemented to ensure finite time convergence of the state vector to the designed SM manifold. A robust exact differentiator is designed to obtain the estimates of the sliding variable and its derivatives. The proposed method is applied to design robust controllers for a power electric system in the presence of the exciter system unmodeled dynamics.

Homogeneous High-Order Sliding Modes

Homogeneity features of dynamic systems are known to provide for a number of general practically important features. In particular, the finite-time convergence is easily proved, and the asymptotic accuracy is readily calculated in the presence of input noises, delays and discrete sampling. General uncertain single-input-single-output regulation problems are only solvable by means of discontinuous control via the so-called high-order sliding modes (HOSM). The homogeneity approach facilitates the design and investigation of new HOSM controllers, featuring such attractive properties as practical continuity of the control in the presence of noises. Robust output-feedback controllers are produced, using robust exact homogeneous differentiators. The asymptotic accuracy of the obtained controllers is the best possible under given circumstances. The dangerous chattering effect is removed by means of a standard procedure. The resulting systems are robust with respect to the presence of unaccounted-for fast stable dynamics of actuators and sensors. Simulation results and applications are presented in the fields of control, signal and image processing.

Sliding Mode Control

Sliding Mode Control

Principles of 2-sliding mode design

Second-order sliding modes are used to keep exactly a constraint of the second relative degree or just to avoid chattering, i.e. in the cases when the standard (first order) sliding mode implementation might be involved or impossible. Design of a number of new 2-sliding controllers is demonstrated by means of the proposed homogeneity-based approach. A recently developed robust exact differentiator being applied, robust output-feedback controllers with finite-time convergence are produced, capable to control any general uncertain single-input–single-output process with relative degree 2. An effective simple procedure is developed to attenuate the 1-sliding mode chattering. Simulation of new controllers is presented.

Higher-order sliding modes, differentiation and output-feedback control

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptotics with respect to input noises and can be used for numerical differentiation as well. The resulting controllers provide for the full output-feedback real-time control of any output variable of an uncertain dynamic system, if its relative degree is known and constant. The theoretical results are confirmed by computer simulation.

Robust exact differentiation via sliding mode technique

The main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises. The proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal. Such an order of the differentiation error is shown to be the best possible one when the only information known on the base signal is an upper bound for Lipschitz’s constant of the derivative.