Robust H ∞ Sliding Mode Control for a Class of Singular Stochastic Nonlinear Systems

The admissible consensus problem of singular multi-agent systems (SMASs) with mismatched norm-bounded parametric uncertainties and unknown norm-bounded disturbances is investigated by an integral sliding mode technique. Under a directed spanning tree network of the state transmission graph, the error states are defined. Then a linear matrix inequality (LMI)-based sufficient condition is presented to guarantee regularity, free impulse, quadratic stability and H ∞ performance of the sliding mode dynamics of the error states.Next, an integral sliding manifold parameter is designed to decrease the order of the LMI caused by the parametric uncertainties, and matrix inversion formulas and inequality techniques are applied to reduce the conservativeness of the LMI. Finally, the control laws, relying on the error states, the property of the state transmission graph and the upper norm bound of disturbances, are presented to ensure the state trajectories of the resulting closed-loop system to achieve robust admissible consensus with H ∞ performance. A simulation example is provided to show the effectiveness of the proposed method.

Section: Resultsmentioning

confidence: 99%

“…Sliding mode control is an effective robust control scheme for uncertain systems and nonlinear systems. An integral sliding surface allows for the exact compensation of uncertainties and perturbations [16,18,25,26]. The sliding motion satisfies some desired specifications such as stability, tracking, regulation, etc.…”

Section: Introductionmentioning

confidence: 99%

Robust admissible consensus of singular multi‐agent systems using sliding mode approach

Yan

2020

“…Consider a DC motor system described in Zhao et al [11], which is illustrated in Figure 6. The dynamic equations for the motions of the system are given as follows:

{\dot{x}}_{1} ((), t) = x_{2} ((), t),

{\dot{x}}_{2} ((), t) = \frac{g}{l} \sin x_{1} ((), t) + \frac{{italicNK}_{m}}{{italicml}^{2}} x_{3},

L_{a} {\dot{x}}_{3} ((), t) = K_{b} {Nx}_{2} ((), t) - R ((), η_{t}) x_{3} ((), t) + u ((), t) + τ ((), t),

y ((), t) = x_{1} ((), t) + τ ((), t),

where x 1 ( t ) = θ p ( t ),

x_{2} ((), t) = {\dot{θ}}_{p} ((), t)

, x 3 ( t ) = I a ( t ), u ( t ) is the control input and τ ( t ) is the external noise.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Singular systems [11], which are also known as descriptor systems, often occur in many areas such as electrical circuit systems, mechanical systems, and economic systems. Singular systems not only can contain conventional state‐space systems as a special case (when the singular matrix is an identity matrix) but also the singular system can contain a special case form in the state space.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy controller design for nonlinear singular systems with external noises subject to passivity constraints

Chang

Varadarajan

2020

This paper applies the state derivative feedback method and proportional plus derivative state feedback method to design the fuzzy controllers for the nonlinear singular systems with external noises. The Takagi‐Sugeno fuzzy modeling technology is employed in this paper to represent the nonlinear singular systems with external noise. Considering the singular Takagi‐Sugeno fuzzy model, the passivity constraint is chosen to treat the external noises for the controlled systems. By using the parallel distributed compensation method, the fuzzy controller is designed to satisfy the Lyapunov stability conditions and passivity constraints simultaneously. These sufficient conditions can be effectively solved in terms of linear matrix inequalities, which can be solved via the convex optimization technique. At last, some numerical examples are provided to verify the applicability and effectivity of the proposed fuzzy controller design methods.

“…H‐infinity controller is used to confirm the robust performance of islanded MG. It is designed based on the H‐infinity norm minimization . The minimizationin of norm may result in conservative controller and indicates the poor performance of the controller .…”

Section: Introductionmentioning

confidence: 99%

Multivariable integral linear quadratic Gaussian robust control of islanded microgrid to mitigate voltage oscillation for improving transient response

Sarker

Badal

Das

et al. 2019

A novel robust integral linear quadratic Gaussian (ILQG) controller is presented in this paper to control the voltage of islanded microgrid and improves its transient response. Microgrid is a small grid that consists of number of distributed generator units, power-electronic components with inductor-capacitor (LC) filters and loads. The loads are parametrically uncertain and unknown that produces the voltage or power oscillation. The ILQG controller is capable to compensate for the voltage oscillation and exhibits the tracking of grid voltage against the different load dynamics. The design of ILQG controller is carried out by augmenting the plant dynamics with an integrator. The robustness of the ILQG controller is studied by considering a number of uncertainties within the plant model. The performance of ILQG controller is compared with linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller in terms of rise time, settling time, bandwidth and tracking error. The comparison results ensure the high bandwidth and tracking performance of ILQG controller as compared to other controllers. KEYWORDS integral linear quadric Gaussian control, microgrid, voltage control