Variable Structure Control Design Research Articles

Robust Controller Design for Uncertain Nonlinear Systems via Fuzzy Modelling Approach with Application to the Stabilization of Power Systems

The robust stabilizing control for nonlinear systems in Takagi-Sugeno fuzzy model with both parameter uncertainties and disturbances is studied in this paper. First, a design method for the stabilizing controllers when only parameter uncertainties exist in the system model is given based on linear matrix inequality technique. Second, a variable structure controller design method for fuzzy systems is presented when there exist both parameter uncertainties and disturbances in the fuzzy model. The proposed theory is applied to the robust stabilizing controller design for the excitation control of power systems. Simulation results show that the transient stability can be improved by using a fuzzy nonlinear controller when there exist both parameter perturbations and external persistent disturbances in the power systems.

Variable Structure Controller Design for Output Tracking of a Class of Discrete-time Nonlinear Systems.

In this paper, a robust controller based on the variable structure control technique for the output tracking of a class of discrete-time uncertain nonlinear systems is developed. An upper bound on the uncertainties is derived to ensure the existence of a quasi-sliding mode in these uncertain systems. Analysis results indicate that the output of the closed-loop system tracks a desired output trajectory and, simultaneously, all signals inside the loop are bounded. Furthermore, the tracking error depends on the proposed controller's parameters. Two examples are given to demonstrate the effectiveness of the proposed control scheme.

Variable structure control of vibration of the simply-supported plates

Robust active vibration control technology is still on its way to develop, though there has been a great number of studies on active vibration control (AVC) topic published since 1980s. The key is to find a good control strategy fitting AVC use and with strong control robustness, in addition to other qualities. As a newer member of robust control strategies, variable structure control (VSC) has attracted control researchers to study its application potentiality at different engineering areas for recent years. Few of them, however, have already paid attention to use in AVC area. In this paper, VSC design methodology used for AVC of a simply-support rectangular plate is investigated. The control design process at the modal state-space is deduced and the matching conditions introduced. Numerically simulated results by using VSC under scheme of the independent modal space control are obtained and compared to those obtained by using least quadratic control and the poles allocation method. It shows that VSC has advantages over the traditional control strategies at control robustness and can control more vibratory modes. [Work supported by the Zhejiang Science and Technology plan fund, PRC.]

Variable Structure Controller Design with Application to Missile Tracking

Variable Structure Controller Design with Application to Missile Tracking

A novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping

This paper presents a new design of adaptive fuzzy variable structure control to solve the traditional problem of model reference adaptive control (MRAC) for a class of single-input, single-output minimum-phase uncertain nonlinear systems via backstepping. Instead of taking the tedious coordinate transformation and yielding a “hard” high-gain controller, we introduce smooth B-spline-type membership functions into the controller so as to compensate for the uncertainties much “softer”, i.e., in a much smoother and locally weighted manner. To be rigorous, it is shown that the stability of the closed-loop system can be assured and the tracking error can globally approach to an arbitrary preset dead-zone range. In order to demonstrate the effectiveness of the developed novel controller, an example is extensively simulated to provide quite satisfactory performance.

Robust Adaptive Variable Structure Control of Spacecraft Under Control Input Saturation

In this paper we propose two globally stable control algorithms for robust stabilization of spacecraft in the presence of control input saturation, parametric uncertainty, and external disturbances. The control algorithms are based on variable structure control design and have the following properties: 1 ) fast and accurate response in thepresenceofbounded external disturbancesand parametricuncertainty;2 )explicit accounting forcontrol input saturation; 3 ) computational simplicity and straightforward tuning. We include a detailed stability analysis for the resulting closed-loop system. The stability proof is based on a Lyapunov-like analysis and the properties of the quaternion representation of spacecraft dynamics. It is also shown that an adaptive version of the proposed controller results in substantially simpler stability analysis and improved overall response. We also include numerical simulations to illustrate the spacecraft performance obtained using the proposed controllers.

Design of adaptive variable structure controllers for perturbed time-varying state delay systems

The problem of stabilizing a class of perturbed linear dynamic systems with time-varying state delay is investigated in this paper. By applying the Lyapunov stability theorem, we develop a delay-independent adaptive variable structure controller to drive the states of system to zero. Based on the variable structure control (VSC) technique, the proposed controller can drive the system into a pre-specified sliding hyperplane to obtain the desired dynamic performance. Once the dynamics of system reach the sliding plane, the proposed controlled system is insensitive to perturbations. The use of adaptive technique is to overcome the unknown upper bound of perturbations so that the reaching condition (or sliding condition) can be satisfied. Furthermore, the globally asymptotic stability is guaranteed for the proposed control scheme under certain conditions. Finally, an example is given to illustrate the feasibility of the proposed control methodology.

Finite dimensional variable structure control design for distributed delay systems

A general design method for the variable structure control of distributed time-delay systems is studied in this paper. The proposed switching function and variable structure controller are of finite dimension. The basic idea is to construct a finite dimensional system which contains all the unstable poles of the original time-delay system and hence those unstable poles of the time delay system will be absorbed by the developed variable structure controller. The proposed method is applied to the stabilization of combustion in a liquid monopropellant rocket motor and satisfactory results are obtained by simulation study. Simulation results show that the developed variable structure controller can still stabilize the combustion when the two key parameters, pressure exponent and maximal time lag r, change from their nominal value down to 0.0 and 0.1 respectively. By this result, we can somewhat overestimate the two parameters to obtain a reliable controller for the rocket motor control systems.

Variable structure control scheme for landing on a celestial object

This paper considers the landing of a space vehicle on a celestial object. By assuming the air drag in two specific forms and the uncertainty in matching type, their effects are studied. Through the construction of a time-varying boundary layer, a new guidance control law for landing on a celestial object is proposed via the variable structure control (VSC) technique to guarantee that tracking performance is achieved at an exponential convergence rate. The proposed guidance law is continuous and alleviates chattering drawback by classic VSC design. Finally, simulation results are presented to illustrate the use of the main design.

Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator

In this paper, a new variable structure control strategy for exponentially stabilizing chained systems is presented based on the extended nonholonomic integrator model, the discontinuous coordinate transformation and the “reaching law method” in variable structure control design. The proposed approach converts the stabilization problem of an n-dimensional chained system into the pole-assignment problem of an ( n−3)-dimensional linear time-invariant system and consequently simplifies the stabilization controller design of nonholonomic chained systems.

Finite-dimensional variable structure control design for systems with a single time delay

A design method for the variable structure control of point time-delay systems is studied in this paper. The proposed switching function and variable structure controller are of finite dimension. The basic idea is to construct a finite-dimensional system which contains all the unstable poles of the original time-delay system and hence those unstable poles of the time delay system will be absorbed by the developed variable structure controller. The proposed method is applied to the stabilization of combustion in a liquid monopropellant rocket motor and satisfactory results are obtained by simulation study. Smooth dependence of the closed-loop system response on the two parameters, the pressure exponent y and time lag ∞, are shown by simulation results.

Nonlinear Control for Missile Terminal Guidance

Variable Structure Control (VSC) technique is applied to the design of robust homing missile guidance laws. In the design procedure, the target’s maneuver is assumed to be unpredictable and is considered as disturbances. Guidance laws are then proposed to achieve the interception performance for both cases of longitude-axis control being available and unavailable. The proposed guidance laws are continuous which alleviate chattering drawback by classic VSC design. Results are obtained and compared with those by realistic true proportional navigation design to illustrate the benefits of the proposed design. [S0022-0434(00)00604-3]

A Sliding Mode Static Output Feedback Controller Based on Linear Matrix Inequalities Applied to an Aircraft System

This paper presents a variable structure control design methodology for multi-input uncertain dynamic systems using only plant output information. Static output feedback is utilized in the design of the switching surface using a Linear Matrix Inequality approach recently proposed in the literature. A novel LMI based optimization approach is subsequently employed in the construction of the control law to guarantee that a sliding motion takes place. The efficacy of the algorithms is demonstrated on a nontrivial design example—an aircraft system representation which includes the flexible modes of the airframe. [S0022-0434(00)00204-5]

Variable structure controller design with H∞ norm and variance constraints for stochastic model reference systems

Based on the concept of variable structure control, this paper investigates the design of the controller u(t) to achieve the error state upper bound covariance control with H∞ norm and variance constraints for a stochastic model reference system. By using the invariance property of variable structure control, the matched reference model input and the plant error term disappear on the sliding mode of the error system. With the aid of the Ito-formula, the controller u(t) is proposed. Combining the sliding phase and hitting phase of variable structure control design, the control feedback gain matrix G is derived to achieve the goals.

Application of lyapunov function method to the design of variable structure control for a class of measure differential systems with impulsive disturbances

It is different from the usually considered systems with norm-bounded uncertainties that the effects of impulsive disturbances always exist in the measure differential systems with impulsive disturbances(MDSID). In the present paper, the Lyapunov function will be used to the design of variable structure control for the MDSID. It will be shown that the given control can counteract the effect of both norm-bounded uncertainties and impulsive disturbances and ensure the asymptotic stability of closed-loop systems. Finally, a simulation result is given to illustrate the effectiveness of the scheme.

Handling actuator non-smooth nonlinearities using variable structure control

This paper deals with robust variable structure control design for continuous-time linear systems involving non- smooth actuator nonlinearities. Also examined in this paper are global boundedness, slabilizability to origin, non-zero set point regulation and arbitrary reference tracking topics when discontinuous controllers are employed within the class of systems studied. Advantages of full-state feedback and robust observer design issues to overcome difficulties introduced into control due to the existence of non-smooth nonlinearities are addressed and the benefits of not having to identify the actual nonlinearity to achieve robust performance within the framework of sliding mode controllers are clarified.

Output feedback variable structure control design for singular systems

In this paper, the problem of output feedback variable structure control design for multivariable linear singular systems is discussed. An algorithm of switching surface design and stability analysis of sliding mode motion are given, the output feedback variable structure control design and global asymptotic stability analysis of closed-loop are given. The control design given in this paper assures that closed-loop trajectory converges to zero with arbitrary exponent speed.

Variable structure control design for uncertain dynamic systems with disturbances in input and output channels

In this paper, a design scheme of variable structure model reference control using only input and output measurements is presented for linear time-invariant systems with uncertain additive and multiplicative dynamics, and disturbances existing in the input and output channels. By introducing auxiliary signals and normalized signals with memory and an appropriate choice of control parameters, the controller guarantees the global stability of the closed-loop system, and the tracking error reach zero in finite time.

Sliding surface design for singularly perturbed systems

The equilibrium manifold of a singularly perturbed system has a close relationship with the sliding surface of a variable structure system (VSS). The fast time and slow timeresponses has a similar behaviour to the 'reaching mode' and 'sliding mode', respectively. This paper aims to equip the powerful composite control method with robustness through variable structure control design. The major bridge in between is a Lyapunov function. It is found that a singularly perturbed system in sliding mode may preserve two-time-scale attribute, in which a new equilibrium manifold exists on the sliding surface. Sliding motions that are attracted to the manifold can therefore be referred to as 'sliding mode in sliding mode'.

An Explicit Formula of Linear Sliding Surfaces for a Class of Uncertain Dynamic Systems with Mismatched Uncertainties

In this note, the problem of designing a variable structure control (VSC) law for uncertain systems where the uncertainty in the state model does not satisfy the matching condition is considered. Based on the LMI approach we develop a new design method of linear sliding surfaces which are linear to the state. We give a sufficient condition for the existence of linear sliding surfaces in terms of LMIs and we give an explicit formula of linear sliding surfaces guaranteeing the quadratic stability of the reduced-order equivalent system dynamics restricted to the sliding surfaces. We also give sufficient conditions for the existence of linear sliding surfaces insuring some pole clustering constraints. Thus, one can easily design VSC laws for a class of uncertain systems with mismatched uncertainties which are difficult to deal with by using conventional VSC design methods. Finally, we give a design example.