State Feedback Strategy Research Articles

Towards generalized synchronization of strictly different chaotic systems

This contribution addresses the problem of the generalized synchronization (GS) in different chaotic systems, and departs from chaotic systems in a triangular from, which can be derived from Lie derivatives. A state-feedback (full knowledge of both master and slave systems) scheme is designed, which achieves GS. The work includes illustrative examples; moreover an experimental setup is used to corroborate the obtained results.

Robust control of a MIMO thermal-hidraulic process with sensor compensation in real time

The main goal of this paper is twofold: To show a kind of robustness in a nonlinear multivariable (NL MIMO) system with feedback control, by employing some linearization and observation techniques well known in reference kind of model; and at the same time it is a proposal to immunize the measurements of a level capacitance-based sensor when there are changes in the measured variables properties, by employing an on-line compensation. The MIMO thermal-hydraulic nonlinear system is stabilized when some linearizing conditions are met and a design methodology for using a state feedback scheme is established. In order to assign poles to the control system, the Jacobian linearization is transformed to the controllable canonical form. This is accomplished by the Brunovsky similarity transformation, and by a static state feedback. A Luenberger observer is added to the control system in order to improve its stability. Illustrations of these techniques are shown via numerical and practical simulations carried out directly in the inexpensive physical process.

A FLEXIBLE NONLINEAR MODEL PREDICTIVE CONTROL SCHEME FOR QUALITY/PERFORMANCE HANDLING IN NONLINEAR SMB CHROMATOGRAPHY

A new state feedback scheme is proposed for the control of simulated moving beds with strongly nonlinear isotherms. The proposed scheme offers a unified framework enabling different performance criteria to be improved according to the active production constraints (achieving low cost, improving efficiency, respecting deadlines) that may unpredictably change during the production batch. The proposed scheme is illustrated through several examples showing the robustness of the closed-loop behavior against parameter uncertainties as well as its reactivity to changes in the active auxiliary criterion.

Hybrid H∞ control based on multiple lyapunov functions

The problem of H ∞ control for switched nonlinear systems is addressed in this paper. Based on multiple Lyapunov functions, a sufficient condition for the problem to be solvable is derived in terms of partial differential inequalities. This condition is a generalization of the well known Hamilton-Jacobi inequalities for the nonlinear H ∞ control problem. The continuous controllers for each subsystem and the switching law are simultaneously designed. As a direct application, a hybrid state feedback strategy is proposed to solve the standard H ∞ control problem for nonlinear systems when no single continuous controller is effective.

Capacity of Memoryless Channels and Block-Fading Channels With Designable Cardinality-Constrained Channel State Feedback

A coding theorem is proved for memoryless channels when the channel state feedback of finite cardinality can be designed. Channel state information is estimated at the receiver and a function of the estimated channel state is causally fed back to the transmitter. The feedback link is assumed to be noiseless with a finite feedback alphabet, or equivalently, finite feedback rate. It is shown that the capacity can be achieved with a memoryless deterministic feedback and with a memoryless device which select transmitted symbols from a codeword of expanded alphabet according to current feedback. To characterize the capacity, we investigate the optimization of transmission and channel state feedback strategies. The optimization is performed for both channel capacity and error exponents. We show that the design of the optimal feedback scheme is identical to the design of scalar quantizer with modified distortion measures. We illustrate the optimization using Rayleigh block-fading channels. It is shown that the optimal transmission strategy has a general form of temporal water-filling in important cases. Furthermore, while feedback enhances the forward channel capacity more effectively in low-signal-to noise ratio (SNR) region compared with that of high-SNR region, the enhancement in error exponent is significant in both high- and low-SNR regions. This indicates that significant gain due to finite-rate channel state feedback is expected in practical systems in both SNR regions.

Output–input stability implies feedback stabilization

We study the recently introduced notion of output–input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. This paper develops the theory of output–input stability in the multi-input, multi-output setting. We show that output–input stability is a combination of two system properties, one related to detectability and the other to left-invertibility. For systems affine in controls, we derive a necessary and sufficient condition for output–input stability, which relies on a global version of the nonlinear structure algorithm. This condition leads naturally to a globally asymptotically stabilizing state feedback strategy for affine output–input stable systems.

Physical Interpretation of State Feedback Controllers to Damp Power System Oscillations

This paper presents a physical interpretation of two state feedback controllers for damping power system electromechanical oscillations. They have been developed by Electricite/spl acute/ de France (EDF). The first one is called the desensitized four loop regulator (DFLR) and it is designed to damp local electromechanical oscillations. It is a robust controller which offers good performance despite the variations of the generator operating conditions. The second controller is called the extended desensitized four loop regulator (EDFLR) and it is designed to address both local and interarea oscillations. The physical interpretation is accomplished converting the state feedback scheme to the standard structure formed by an automatic voltage regulator (AVR) plus a power system stabilizer (PSS). Two widely used PSS design methods based on eigenvalue sensitivities and frequency response are reviewed to obtain the interpretation. The DFLR can be interpreted as a controller which provides the suitable phase compensation according to these two PSS design methods over a wider frequency range. The EDFLR can be interpreted as a controller which maximizes its robustness under uncertainties at both PSS output and the input of the plant.

Superharmonic resonance bifurcation control of parametrically excited system based on state feedback strategy

A nonlinear parametric feedback control is propo sed to modify the steady-state resonance responses, thus to reduce the amplitude of the response and to eliminate the saddle-node bifurcations that take place i n the resonance responses. The nonlinear gain of the feedback control is determi ned by analyzing the bifurcation function associated with the corresponding freq uency-response equation and the Jacobian matrix. It is shown by illustrative exa mples that the proposed nonlinear feedback is effective for controlling superhar monic resonance responses.

A state tracking control algorithm with pole assignment

In this paper, a systematic state feedback scheme is proposed to arbitrarily place all the closed-loop poles of linear multivariable systems. The systems considered are linear time-invariant and completely state controllable. The state feedback gain matrix can be formulated using an algebraic approach. A general state tracking controller is further developed. Zero steady-state errors are guaranteed. The speed control of a vertical take-off and landing aircraft is carried out to show the effectiveness of the proposed state tracking and pole assignment schemes.

A note on stability, robustness and performance of output feedback nonlinear model predictive control

In recent years, nonlinear model predictive control (NMPC) schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in the framework of nonlinear predictive control. This paper combines stabilizing instantaneous state feedback NMPC schemes with high-gain observers to achieve output feedback stabilization. For a uniformly observable MIMO system class it is shown that the resulting closed loop is asymptotically stable. Furthermore, the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme can be recovered to any degree of accuracy for large enough observer gains, thus leading to semi-regional results. Additionally, it is shown that the output feedback controller is robust with respect to static sector bounded nonlinear input uncertainties.

A Design Method of Perfect Tracking Control for Discrete-Time Systems Using Multi-Rate Control

This paper presents a design method of perfect tracking control, for discrete-time systems based on multi-rate control. Generally, perfect tracking control schemes cannot be applied to nonminimum phase plants because of unstable pole-zero cancellations. Some methods that are applicable to nonminimum phase plants have been proposed, however, the following problems are left unsolved : limitations to plants and unclearness of design freedoms. We propose to use multi-rate control systems and state feedback schemes for perfect tracking. Since the method has been stated in 2-degree of freedom control techniques in this paper, it is clear how the design freedoms will be reserved after the design of tracking control. Basic techniques of this scheme have been presented, however, they cannot be applied to nonminimum phase discrete-time systems. We propose techniques that are applicable to nonminimum phase discrete-time systems. Finally, computer simulation results are presented.

FUZZY-SLIDING STATE-FEEDBACK CONTROL OF NONLINEAR BALL SUSPENSION SYSTEM

This paper presents a fuzzy-sliding control, based on state feedback methods, to control nonlinear magnetic ball suspension system. Simulations results show that the control speed of fuzzy-sliding-mode controllers is more than the classical sliding mode controllers, but the steady state error of later is less that the earlier. This is due to the limited number of membership functions defined for the input variables of the system. Here, a combination of fuzzy-sliding-mode and state-feedback control is presented. Simulation results show that this controller contains the advantages of both the fuzzy-sliding-mode method (fast response) and the state-feedback scheme (low steady-state error).

On output feedback nonlinear model predictive control using high gain observers for a class of systems

In recent years, nonlinear model predictive control schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in connection to nonlinear predictive control. Most of the existing approaches for output feedback nonlinear model predictive control do only guarantee local stability. Here we consider the combination of stabilizing instantaneous NMPC schemes with high gain observers. For a special MIMO system class we show that the closed loop is asymptotically stable, and that the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme are recovered for a high gain observer with large enough gain and thus leading to semi-global/ non-local results.

Static Output Feedback: An Approach to Compare Optimal Partial State Linear Controllers

The design and implementation of the optimal partial state or output feedback controllers have significant importance in applications when access to the full state is not possible either due to the dynamical system constraints or the control system requirements. In this paper, partial state feedback strategies are implemented to minimize prescribed performance criteria that has applicability in active vibration control. The partial state feedback problem is posed as static output feedback. A solution to this problem using a numerical optimization technique is fOund.

Minimization of the worst case peak-to-peak gain via dynamic programming: state feedback case

Considers the problem of designing a controller that minimizes the worst case peak-to-peak gain of a closed-loop system. In particular, we concentrate on the case where the controller has access to the state of a linear plant and it possibly knows the maximal disturbance input amplitude. We apply the principle of optimality and derive a dynamic programming formulation of the optimization problem. Under mild assumptions, we show that, at each step of the dynamic program, the cost to go has the form of a gauge function and can be recursively determined through simple transformations. We study both the finite horizon and the infinite horizon case under different information structures. The proposed approach allows us to encompass and improve earlier results based on viability theory. In particular, we present a computational scheme alternative to the standard bisection algorithm, or gamma iteration, that allows us to compute the exact value of the worst case peak-to-peak gain for any finite horizon. We show that the sequence of finite horizon optimal costs converges, as the length of the horizon goes to infinity, to the infinite horizon optimal cost. The sequence of such optimal costs converges from below to the optimal performance for the infinite horizon problem. We also show the existence of an optimal state feedback strategy that is globally exponentially stabilizing and derive suboptimal globally exponentially stabilizing strategies from the solutions of finite horizon problems.

Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition

Proper orthogonal decomposition (POD) is a method to derive reduced-order models for dynamical systems. In this paper, POD is utilized to solve open-loop and closed-loop optimal control problems for the Burgers equation. The relative simplicity of the equation allows comparison of POD-based algorithms with numerical results obtained from finite-element discretization of the optimality system. For closed-loop control, suboptimal state feedback strategies are presented.

Static and dynamic state feedback control model of basal ganglia-thalamocortical loops.

It is argued that a novel control architecture, the Static and Dynamic State (SDS) feedback scheme, which utilizes speed-field tracking, exhibits global stability, and allows on-line tuning by any adaptation mechanism without canceling stability if certain structural conditions are met, can be viewed as a model of basal ganglia-thalamocortical loops since (1) the SDS scheme predicts the neuronal groups that fit neuronal classification in the supplementary motor area, the motor cortex and the putamen, (2) the structural stability conditions require parallel channels, a feature that these loops provide, and (3) the SDS scheme predicts two major disorders that can be identified as Parkinson's and Huntington's diseases. Simulations suggests that the basal ganglia work outside the realm of the stability condition allowed by the robustness of the scheme and required for increased computation speeds.

Time-varying feedback control of nonaffine nonlinear systems without drift

Sufficient conditions are presented under which a general nonlinear system without drift is globally asymptotically stabilizable by time-varying state feedback. A novel approach is developed for the design of a time-varying smooth state feedback controller. The controller is explicitly constructed by using the bounded state feedback strategy (Lin, 1995, 1996) combined with Lyapunov technique as well as lossless systems theory. This work incorporates earlier global stabilization results (Coron, 1992; Pomet, 1992) for controllable affine systems without drift, which are known not to be smoothly stabilizable via any time-invariant state feedback.

A SMART PNEUMATIC SERVO POSITIONING AXIS AND ITS APPLICATIONS

A smart digital controller for pneumatic servo positioning axis is discussed in this paper. The controller is based on a non-linear state feedback control algorithm and it has much intelligence. Through close theoretical analysis and a large amount of experiments a concept is developed, which lets the controller itself find the optimal control parameterset according to the system data given quite easily by a user. With the controller, satisfactory characteristics can always be obtained even for those pneumatic servo axes with lage variations in dimension or working under some extreme special conditions, e. g. for cylinder length from 50mm to 3000mm, diameter from 16mm to 125mm or mass load from 0.5 KG to 1500 KG.In this paper, theories for modelling and design of the controller are given and the principles of the non-linear state feedback strategy are discussed. Some intelligent algorithms employed in the controller to further improve the dynamic and static performances of a pneumatic servo positioning axis are also reported. Finally, a brief description of some additional important features of the controller and several practical applications are introduced.

An AC voltage switching regulator with instantaneous output voltage control

This is the first attempt to control the instantaneous output of an ac/ac direct power converter. The ac chopper-type regulator has the potential ability of quick response to the control command. However, detecting the mean or effective value of the ac output voltage, as is commonly done in the conventional closed-loop ac regulators, greatly degrades the inherent fast response capability of the chopper circuit. The proposed ac switching regulator adopts the Cuk converter for the main circuit and an instantaneous voltage control technique. A practical state feedback scheme together with the integral control was devised to stabilize the system and also minimize the steady-state error. The response speed is so fast (about 300 μs with resistive load) that the converter can produce a sinusoidal output voltage even from a distorted source voltage. The four-quadrant operation can handle any kind of ac load. A complete analytical description and relevant design data of this new regulator are provided with some experimental results.