Sliding Mode Control and State Estimation for a Class of Nonlinear Singularly Perturbed Systems

This paper is concerned with the problem of designing a robust output tracking controller for MIMO nonlinear systems with weakly non-minimum phase. Based on our system formulation, control plants with uncertainties and/or with actuator dynamics fall into the class under consideration. The controller design here is divided into two phases: fast feedback control and slow feedback control, so that a final composite control is obtained. The former is chosen to stabilize the boundary layer system, whereas the latter essentially handles the mismatched uncertainties after the system is reformulated. Under some mild assumptions, it is shown that the overall states are bounded and the tracking errors converge to a residual set whose size is a class k function of e. As e → 0, the residual set shrinks to the origin. An interesting application to a simplified aircraft model with fast actuator dynamics, which turns out to be weakly non-minimum phase, is given. The computer simulation has verified the expected satisfac...

To eliminate the effect of the uncertain disturbances and improve the control accuracy of spacecraft Attitude Control System, a nonlinear control algorithm named nonsingular terminal sliding-mode feedback controller is proposed in this work, which is mainly made up of nonsingular terminal sliding-mode controller and sliding-mode feedback controller. In the first place, nonsingular terminal sliding-mode controller is designed, which guarantees global asymptotic convergence of the attitude in the presence of the uncertain perturbations from the space. Despite that, it is the influence of the uncertain disturbances that hinder the control accuracy. Then, in order to promote the control accuracy, the sliding-mode feedback controller based on the principle of minimum sliding-mode error is proposed, which is used to compensate the control errors of the nonsingular terminal sliding-mode controller caused by the uncertainties. Hence, the determination principle of the weighting matrix in sliding-mode feedback controller is discussed, and the algorithm structure of the sliding-mode feedback controller is also analyzed, which provides the theoretical basis for the sliding-mode feedback controller. By contrast, an adaptive fuzzy algorithm is designed and introduced into the nonsingular terminal sliding-mode controller to improve the control accuracy, which named the nonsingular terminal fuzzy sliding-mode controller. Last but not the least, several numerical examples are presented to demonstrate the efficacy of the proposed nonsingular terminal sliding-mode feedback controller. Simulation results confirm that the control accuracy of the nonsingular terminal sliding-mode feedback controller is higher than the nonsingular terminal sliding-mode controller and the same as nonsingular terminal fuzzy sliding-mode controller. Not only is the calculation of the nonsingular terminal fuzzy sliding-mode feedback controller smaller than nonsingular terminal fuzzy sliding-mode controller, the adjusted parameters are also fewer than nonsingular terminal fuzzy sliding-mode controller obviously. The numerical results clearly indicate that the proposed nonsingular terminal sliding-mode feedback controller based on the principle of minimum sliding-mode error can compensate control errors accurately and quickly; therefore, it can reduce the effect of the uncertainties from the space indirectly.

Design of feedback control, for a system with slow and fast eigenvalue modes, using single sampling rate results in either information loss (for a larger sampling period) or increased computations (for a smaller sampling period). This paper contributes to designing multirate state feedback controllers for such systems. In this, it is shown that the feedback control for a linear time-invariant system, having slow and fast eigenvalue modes, can be successfully designed by multirate sampling of states in two stages. Multirate sampling refers to sampling slow- and fast-varying states at different rates, that is sampling slow states at a lower rate than the fast states. Here, two approaches for multirate sampling of states are presented, depending on the sampling sequence. In the first approach, fast subsystem states are sampled initially, and then, slow subsystem states are sampled, whereas in the second approach, slow subsystem states are sampled before sampling the fast subsystem states. As far as the two-stage design is concerned, the first stage of the design of feedback control is initiated just after sampling the first subsystem. Then, the left subsystem is sampled, and the second stage of the design of feedback control is accomplished. It is proved that the feedback controls derived with the multirate sampling of states stabilize the full-order system in both approaches. The design and implementation aspects of both approaches are compared. Finally, the applicability of the proposed control is demonstrated by simulating two examples. Simulations are also compared with other methods proposed in the literature.

The dynamics of a web transport system are coupled and interactive among spans of web and rolls/rollers. As the process speed or variation of the speed is high, system friction and inertia of rotation of rolls could cause problems in implementation of observer techniques for tension estimation and control. In the author's previous study (see IEEE International Conference on Industrial Electronics, Control and Instrumentation, Denver, Colorado, USA (2001)), an observer-based tension feedback controller with friction and inertia compensation was proposed. However, the gains of observer and controller were determined based on the trial-and-error approach. This paper continues the author's previous study and presents an analytical approach for the gain design of observers in the time domain but design of controllers in the frequency domain. The linearization and decentralization techniques are implemented. Design of tension observers and feedback controllers with friction and inertia compensation is studied. Approaches for the gain design are discussed, and summarized procedures are given. The proposed analytical approach for design of tension observers and feedback controllers has been proven to be adequate by experiment.

In the process of avalanche injection of electrons into silicon dioxide, besides electron trapping in the bulk of the oxide, there are slow and fast interface states generated. The slow states are donors and positively charged when empty. Together with positive charge in the interface states, they compensate the negative bulk charge to give the turn-around effect. The final C-V curve is due to a complex sum of different charge components. The slow states can be discharged when heated under +5 V or higher biases at 160 °C or above. The final charge state is only semipermanent. Fast interface states are also annealed in the process, and the anneal is enhanced by a positive bias. Bulk trapped electrons are minimally perturbed by the anneal. It is postulated that the slow states may communicate with silicon through the fast interface states in a thermally activated process. In order to study bulk electron trapping, avalanche injection should be carried out at elevated temperatures.

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Contribution of fast and slow states to Negative Bias Temperature Instabilities in HfxSi(1-x)ON/TaN based pMOSFETs

Approximations and uncertainties in system modeling lead to inaccurate state estimation and thereby the failure of systematically designed control techniques. A robust control technique is therefore needed for state estimation and control when the system is complex and is accompanied by uncertainties. One of the robust control techniques is sliding mode control (SMC). Sliding mode control is a non-linear control technique with remarkable properties like robustness and insensitive to disturbances. Hence, it is highly recommended for the control of extremely complex plants, like nuclear reactors. However, chattering is one of the main disadvantages that arise while using a sliding mode control. In this paper, a sliding mode technique is used for estimating neutron precursor density, xenon, and iodine concentrations which otherwise are very difficult to measure, and then a sliding mode controller with a reduced chattering effect is proposed for pressurized water reactor (PWR). Stability analysis of the system is carried out using the Lyapunov approach. Simulation results are presented to show the efficiency of the proposed system.

Three-phase induction motors have been widely used in a variety of industrial applications. Induction motors have been able to incrementally improve energy efficiency to satisfy the requirements of reliability and efficiency, Melfi et al. (2009). There are well known advantages of using induction motors over permanent magnet DCmotors for position control tasks; thus, efforts aimed at improving or simplifying feedback controller design are well justified. There exists a variety of control strategies that depend on difficult to measuremotor parameters while their closed loop behavior is found to be sensitive to their variations. Even adaptive schemes tend to be sensitive to speed-estimation errors, yielding to a poor performance in the flux and torque estimation, especially during low-speed operation, Harnefors & Hinkkanen (2008). Generally speaking, the designed feedback control strategies have to exhibit a certain robustness level in order to guarantee an acceptable performance. It is possible to (on-line or off-line) obtain estimates of the motor parameters, Hasan H Toliyat et al. (2003), but some of them can be subject to variation when the system is undergoing actual operation. Frequent misbehavior is due to external and internal disturbances, such as generated heat, that significantly affect some of the system parameter values. An alternative to overcome this situation is to use robust feedback control techniques which take into account these variations as unknown disturbance inputs that need to be rejected. In this context, sliding mode techniques are a good alternative due to their disturbance rejection capability (see for instance, Utkin et al. (1999)). In this chapter, we consider a two stage control scheme, the first one is devoted to the control of the rotor shaft position. This analog control is performed bymeans of the stator current inputs, in a configuration of an observer based control. Themathematical model of the rotor dynamics is a simplified model including additive, completely unknown, lumping nonlinearities and external disturbances whose effect is to be determined in an on-line fashion by means of linear observers. The gathered knowledge will be used in the appropriate canceling of the assumed perturbations themselves while reducing the underlying control problem to a simple linear feedback control task. The control scheme thus requires a rather reduced set of parameters to be implemented. Sliding Mode Control Design for Induction Motors: An Input-Output Approach 7

This article presents an original motion control strategy for robot manipulators based on the coupling of the inverse dynamics method with the so-called second-order sliding mode control approach. Using this method, in principle, all the coupling non-linearities in the dynamical model of the manipulator are compensated, transforming the multi-input non-linear system into a linear and decoupled one. Actually, since the inverse dynamics relies on an identified model, some residual uncertain terms remain and perturb the linear and decoupled system. This motivates the use of a robust control design approach to complete the control scheme. In this article the sliding mode control methodology is adopted. Sliding mode control has many appreciable features, such as design simplicity and robustness versus a wide class of uncertainties and disturbances. Yet conventional sliding mode control seems inappropriate to be applied in robotics since it can generate the so-called chattering effect, which can be destructive for the controlled robot. In this article, this problem is suitably circumvented by designing a second-order sliding mode controller capable of generating a continuous control law making the proposed sliding mode controller actually applicable to industrial robots. To build the inverse dynamics part of the proposed controller, a suitable dynamical model of the system has been formulated, and its parameters have been accurately identified relying on a practical MIMO identification procedure recently devised. The proposed inverse dynamics-based second-order sliding mode controller has been experimentally tested on a COMAU SMART3-S2 industrial manipulator, demonstrating the tracking properties and the good performances of the controlled system.

Variable structure control with sliding mode, which is commonly known as sliding mode control (SMC), is a nonlinear control strategy that is well known for its robust characteristics (Utkin, 1977). The main feature of SMC is that it can switch the control law very fast to drive the system states from any initial state onto a user-specified sliding surface, and to maintain the states on the surface for all subsequent time (Utkin, 1977), (Phuah et al., 2005 a). The conventional SMC has two disadvantages (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), which are the chattering phenomenon (Slotine & Sastry, 1983), (Young et al., 1999) and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), (Hussain & Ho, 2004). Many methods of SMC using neural networks (NN) have been proposed (Phuah et al., 2005 a), (Ertugrul & Kaynak, 2000), (Hussain & Ho, 2004), (Phuah et al., 2005 b), (Yasser et al., 2007), (Topalov et al., 2007). In this paper, sliding mode controls using NN are proposed to deal with the problem of eliminating the chattering effect and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant. The first method of this method applies a method using a simplified form of the distance function proposed in (Phuah et al., 2005 a), (Phuah et al., 2005 b). Furthermore, the simplified distance function of our method uses a sliding surface in the space of the output error and its derivations, as proposed in (Yasser et al., 2006 a), (Yasser et al., 2006 c), instead of the space of the states error to construct a corrective control input. Thus, no observer is required in the proposed method. Moreover, we also propose the application of an NN to construct the equivalent control input of SMC. The weights of the NN are adjusted using a backpropagation algorithm as in (Yasser et al., 2006 b). Hence, a thorough knowledge of the parameters and dynamics of the nominal controlled plant is not required for calculating the equivalent control law. Finally, a stability analysis is carried out, and the effectiveness of this first control method is confirmed through computer simulations. This first method has been previously discussed in (Yasser et al., 2007). The second method of this paper applies an NN to produce the gain of the corrective control of SMC. Furthermore, the output of the switching function the corrective control of SMC is applied for the learning and training of the NN. There is no equivalent control of SMC is used in this second method. As in the first method, this second method applies a method using a sliding surface in the space of the output error and its derivations, as proposed in

Sliding-mode direct torque control and sliding-mode observer with a magnetizing reactance estimator for the field-weakening of the induction motor drive

In this paper, an adaptive iterative learning control (AILC) method combined with sliding mode technique is proposed to improve the force control performance for repeating tasks of fluidic muscle (FM) driven parallel manipulators. Different from the traditional iterative learning control method, the proposed AILC is to learn the controller time-varying parameters rather than to learn the control signals. Since the AILC is sensitive to non-repetitive disturbances, the sliding mode technique is introduced to enhance the robustness. Since no model information involved in the controller design, the proposed method is a complete data-driven method. Hence, the difficulty of obtaining accurate model is avoided. Simulation studies are performed on a two degrees of freedom FM driven parallel manipulator. Simulation results demonstrate that the proposed method can achieve high force tracking performance and robustness.

This paper decomposes nonlinear 2-order Hamiltonian dynamics into a hierarchy of two 1-order complex component dynamics. This allows the stability of the 2-order dynamics to be assessed based on the two nonlinear 1-order complex dynamics, using the tools of contraction theory. This decomposition is a tensor result, independent of the chosen coordinate system. It extends well-known Lyapunov asymptotic stability results, based on energy dissipation, to the exact characterization of exponential convergence rates for damped non-autonomous Hamiltonian systems. Specifying the nonlinear damping and complex action φ is sufficient to tune the performance of an associated observer or controller design. Explicit exponential stability guarantees are then given based on the second covariant derivative of φ. The result allows state and time-dependent complex exponential convergence or contraction rates to be placed exactly in a controller or observer design. As such, it extends linear time-invariant eigen-value placement to time-varying or state-dependent eigen-values. Simple applications include state-dependent eigen-value placement for an aircraft or an inverted pendulum controller. The corresponding observer design is illustrated for the Mach-dependent vertical channel dynamics of the strap-down navigation system in polar regions.

<div class="htmlview paragraph">This article describes an application of <i>sliding mode</i> techniques to the design of an air/fuel ratio control system for a 4-stroke engine, to minimize exhaust gas and emissions.</div> <div class="htmlview paragraph">This technique allows to achieve good control performance in terms of precision, robustness, and fast transient response.</div> <div class="htmlview paragraph">To support <i>sliding mode control</i> a second PI stage was added, based on the signal of a second oxygen sensor installed after the catalytic converter.</div> <div class="htmlview paragraph">Experimental results were better than those obtained with a conventional PI control, currently used on production applications.</div> <div class="htmlview paragraph">The new control algorithm (<i>sliding mode</i> based on the first oxygen sensor, and PI on the second) is very versatile because the approach chosen allows to calculate the parameters values for the ECU using computer simulation.</div>