Showing papers on "Separation principle published in 1996"

Robust motion controller design for high-accuracy positioning systems

Abstract: This paper presents a controller structure for robust high speed and accuracy motion control systems. The overall control system consists of four elements: a friction compensator; a disturbance observer for the velocity loop; a position loop feedback controller; and a feedforward controller acting on the desired output. A parameter estimation technique coupled with friction compensation is used as the first step in the design process. The friction compensator is based on the experimental friction model and it compensates for unmodeled nonlinear friction. Stability of the closed-loop is provided by the feedback controller. The robust feedback controller based on the disturbance observer compensates for external disturbances and plant uncertainties. Precise tracking is achieved by the zero phase error tracking controller. Experimental results are presented to demonstrate performance improvement obtained by each element in the proposed robust control structure.

Mathematical theory of control systems design

Abstract: Preface. Introduction. Part One: Stability of control systems. I. Continuous and discrete deterministic systems. II. Stability of stochastic systems. Part Two: Control of deterministic systems. III. Description of control problems. IV. The classical calculus of variations and optimal control. V. The maximum principle. VI. Linear control systems. VII. Dynamic programming approach. Sufficient conditions for optimal control. VIII. Some additional topics of optimal control theory. Part Three: Optimal control of dynamical systems under random disturbances. IX. Control of stochastic systems. Problem statements and investigation techniques. X. Optimal control on a time level of random duration. XI. Optimal estimation of the state of the system. XII. Optimal control of the observation process. Part Four: Numerical methods in control systems. XIII. Linear time-invariant control systems. XIV. Numerical methods for the investigation of nonlinear control systems. XV. Numerical design of optimal control systems. General references. Subject index.

Sliding mode observer for triangular input form

Abstract: This paper discusses the problem of designing an observer for nonlinear systems. In Drakunov and Utkin (1995) a new concept of sliding observers was introduced, where the key point is that the equivalent control concept is extensively used. Moreover, in Boukhobza, Djemai, and Barbot (1996) we use a classical sliding mode observer in order to design an observer for the largest class with the so-called output injection form. Here, our purpose is to discuss the observer design for a system in a triangular input observer form. For a system in a triangular input observer form there is no problem of singular input. The second purpose of this paper is to show how to use the anti-peaking sliding method in the case of successive equivalent vectors.

Robust output tracking using a sliding mode controller/observer scheme

Abstract: A controller/observer pair is presented, on the basis of sliding mode ideas, which provides robust output tracking of a reference signal using only measured output information. Closed-loop analysis indicates that asymptotic tracking of a constant reference signal will be achieved despite the presence of a class of matched uncertainty. Furthermore, a form of ‘separation principle’ is shown to hold for this class of controller and observer, in the sense that they can be designed independently apart from a scalar function of the uncertainty bounds.

Partially Observed Differential Games, Infinite-Dimensional Hamilton--Jacobi--Isaacs Equations, and Nonlinear $H_\infty$ Control

Abstract: This paper presents new results for partially observed nonlinear differential games. Using the concept of information state, we solve this problem in terms of an infinite-dimensional partial differential equation, which turns out to be the Hamilton--Jacobi--Isaacs (HJI) equation for partially observed differential games. We give definitions of smooth and viscosity solutions and prove that the value function is a viscosity solution of the HJI equation. We prove a verification theorem, which implies that the optimal controls are separated in that they depend on the observations through the information state. This constitutes a separation principle for partially observed differential games. We also present some new results concerning the certainty equivalence principle under certain standard assumptions. Our results are applied to a nonlinear output feedback $H_\infty$ robust control problem.

A model reference observer for time-delay control and its application to robot trajectory control

Abstract: This paper addresses the estimation problem of the states and their derivatives for time-delay control (TDC), a robust control technique for nonlinear systems To this end, an observer design method is presented In addition, the sufficient conditions are discussed and implementation issues are addressed Finally, experiments were undertaken on a SCARA-type robot subject to substantial inertia variations and external disturbances The results showed that the controller/observer performs quite robustly under inertia variations and disturbances and is much less sensitive to sensor noise than the controller using numerical differentiations

Maximum principle for optimal control of stochastic system of functional type

Abstract: In this paper, the maximum principle for optimal control of stochastic systems of functional type is obtained. We also derived the adjoint equation which seems to be new in form and proved the existence and uniqueness of the solution of that equation.

Time-scale separation and robust controller design for uncertain nonlinear singularly perturbed systems under perfect state measurements

Abstract: We study time-scale separation and robust controller design for a class of singularly perturbed nonlinear systems under perfect state measurements. The system dynamics are taken to be jointly linear in the fast state variables, control and disturbance inputs, but nonlinear in the slow state variables. Since global timescale separation may not always be possible for nonlinear singularly perturbed systems, we restrict our attention here to some closed subset of the state space, on which a timescale separation holds for sufficiently small values of the singular perturbation parameter. We construct a slow controller and a composite controller based on the solutions of particular slow and fast games obtained using time-scale separation. For the class of systems for which the slow controller can be selected to be robust with respect to small regular structural perturbations on the slow subsystem, we show under some growth conditions that the composite controller can achieve any desired level of performance that is larger than the maximum of the performance levels for the slow and fast subsystems,. A slow controller, however, is not generally as robust as the composite controller; but, still under some conditions which are delineated in the paper, the fast dynamics can be totally ignored. The paper also presents a numerical example to illustrate the theoretical results.

Nonlinear discrete‐time risk‐sensitive optimal control

Abstract: SUMMARY This paper is devoted to the study of the connections among risk-sensitive stochastic optimal control, dynamic game optimal control, risk-neutral stochastic optimal control and deterministic optimal control in a nonlinear, discrete-time context with complete state information. The analysis worked out sheds light on the profound links among these control strategies, which remain hidden in the linear context. In particular, it is shown that, under suitable parameterizations, risk-sensitive control can be regarded as a control methodology which combines features of both stochastic risk-neutral control and deterministic dynamic game control.

Feedback control of state constrained optimal control problems

Abstract: Solutions to nonlinear optimal control problems are usually computed in open-loop form, especially if the problem is subjected to state constraints. Open-loop controls, however, are not very useful from a control perspective due to their lack of robustness. We discuss a couple of useful techniques which reduce a state-constrained problem into an unconstrained problem, and subsequently apply a technique to synthesize an optimal state feedback controller for the reduced problem. The controller is able to recover the open-loop optimal state and control for arbitrary initial conditions arising from a nontrivial subset of the state space, while ensuring that the state constraint is satisfied at all time.

DSP based field-oriented control of induction motor with a nonlinear state observer

Abstract: The paper deals with the implementation of a standard field-oriented induction motor control with a rotor flux nonlinear state observer, similar in structure to the well known Luenberger observer for a linear system. The real time control hardware used to implement the field oriented control and the nonlinear observer consists of a data translation single board DSP data acquisition system based on a TMS 320C40. After a brief description of the observer features and the proposed system, the experimental set-up is presented and discussed in detail. Experimental results demonstrate its excellent low sensitivity to rotor resistance variation in comparison to a field-oriented control system based on conventional current model flux estimation.

On the stability of nonlinear plants that include an observer for their feedback linearization

Abstract: The states of a plant are required to achieve exact linearization via state feedback and transformation. This calls for an observer when all the plant states are not directly accessible, then the linearizing feedback law can be implemented with the observer estimates. We analyse this situation from a stability point of view, for a class of nonlinear systems and a class of observers. Morever, we set a sufficient condition that makes possible the stabilization of the whole feedback system: the plant, the observer and the (linearizing) feedback law. From this condition, which depends on the observer gains and the linear feedback gains, we find a region for these parameters where the stability of the whole system is guaranteed.

Observer design for discrete nonlinear descriptor systems

Abstract: A nonlinear observer is considered for a class of discrete nonlinear descriptor systems subject, to unknown inputs and faults. This class is partly characterized by globally Lipschitz nonlinearities, and a member system may be singular and possibly non-causal. The structure proposed for the observer makes it useful for both state estimation for feedback controls and residual generation for fault detection. Results on the existence of solutions are given and some useful bounds are derived which are important in the observer design. The proposed nonlinear observer is based on a transformed system and on the solution of a Riccati equation. The existence, convergence properties and robustness of the observer are investigated by the use of a quadratic Lyapunov function. A design algorithm is given and applied to the estimation of the states of a flexible joint robot.

Observer-Based Feedback Linearizing Control of an Electromagnetic Suspension

Abstract: This paper develops a stabilizing observer-based feedback linearizing controller for a single-axis electromagnetic suspension. The controller uses only the measured output ofthe system, and is shown to be robust with respect to parameter uncertainty. The controller differs from other robust feedback linearizing controllers that have appeared in recent literature, because it is continuous, and non-adaptive. Lyapunov's second method is used to prove stability and robustness of the controller. The controller has a simple structure and its gains are determined by solving two weakly coupled Riccati equations. Numerical simulations are performed to compare a linear feedback controller and the observer-based feedback linearizing controller. Results obtained demonstrate that the nonlinear controller yields superior performance when compared with the linear feedback controller. The controller synthesis technique developed in this paper is applicable to other fully feedback linearizable systems, not just electromagnetic suspensions.

Maximum Principle for the Optimal Control of a Hyperbolic Equation in Two Space Dimensions

Abstract: A maximum principle is developed for a class of problems involving the optimal control of a damped parameter system governed by a not-necessarily separable linear hyperbolic equation in two space d...

Neural Adaptive Feedback Linearization Control

Abstract: The design of a controller for a process is most usually based on a mathematical model of the process. Obtaining such a model can be a difficult task : process parameters can be uncertain or the underlying principles of the process are not fully understood (resulting in a incomplete model of the process). When only an incomplete model is available special controller design techniques are necessary for designing a controller which causes a stable control behavior with good performance. In this paper we present an indirect adaptive controller based on the principle of feedback linearization and which uses neural networks. This controller can be applied to a certain class of nonlinear systems. It is shown that the controller is stable in the sense of Lyapunov. Several simulation examples are included to make the theory more transparent.

State observer design using deterministic least squares technique

Abstract: The design of a state observer is treated as a problem of determining a solution to a system of linear equations. The state observer is readily obtained by using least squares techniques. The state estimation horizon, which determines the number of past measurement samples used to reconstruct the state vector, is introduced as a tuning parameter for the proposed state observer. A stability result concerning the choice of the state estimation horizon is established. It is also shown that both the steady state Kalman filter and the moving window state observer can be recovered from this deterministic least squares setting. A feature of this deterministic formulation is the conceptual simplicity of the derivation. Furthermore multivariable, or even multirate systems can be handled in a transparent manner without additional complexity.

Integrated control and fault diagnosis design: a polynomial approach

Abstract: A design method is presented which integrates control action and fault detection and isolation. Control systems operating under potentially faulty conditions are considered, and it is demonstrated how to design a single unit which handle both the required control action, as well as identifying faults occurring in actuators and sensors. This unit is able to: 1) follow references and reject disturbances robustly; 2) control the system such that undetected failures do not have disastrous effects; 3) reduce the number of false alarms; and 4) identify which faults have occurred. The method uses a type of separation principle which makes the design process very transparent, and a polynomial H/sub /spl infin// formulation which makes weight selection straightforward. As a consequence of the separation between control and diagnosis, we prove that the controller needs not be detuned in order to get good diagnosis results, in contrast to common beliefs.

A behavioral approach to the l1 optimal control problem

Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Design of mixed H2/mu controllers using a separation principle

Abstract: This paper considers the design of H2/mu controllers. These controllers guarantee both stability and a minimum level of H2 performance for allowable levels of uncertainty. The controllers have previously been derived via the solution to a convex linear matrix inequality problem. This paper presents an alternative derivation for the controllers which relies upon separating the problem into a full state feedback problem and an output estimation problem. This leads to a set of three coupled Riccati equations, which, in some cases, are shown to be able to be solved more quickly than the comparable LMI problem. (Author)

Output-Driven Minimal Controller Synthesis with an Adaptive Observer

Abstract: This paper describes how the minimal controller synthesis (MCS) algorithm is combined with the minimal observer synthesis (MOS) algorithm to produce an output feedback control structure in which no prior knowledge of plant state parameters is required. While the principal results relate to single-input single-output (SISO) systems, extensions to a particular class of multi-variable systems is discussed. Implementation and simulation examples are included to illustrate the effectiveness of the proposed scheme.

The design method of two-degree-of-freedom controller using /spl mu/-synthesis and its application to two-mass system

Abstract: This paper presents the design method of two-degree-of-freedom (2 dof) controller system based on the internal structure Firstly, we show the internal structure of the system and derive the condition which clearly shows the equivalence between the disturbance observer based controller and the generalized 2 dof controller. Secondly, we propose the design method of free parameter using /spl mu/-synthesis taking into account the structure of the system and the tuning of the Q so as to satisfy the derived conditions. Finally, we show some simulation results of velocity control of a 2-mass system and confirm the effectiveness of the proposed method.

Nonlinear transition controller design using neural networks tested on a polymerization reactor

Abstract: We propose a complete scheme for a nonlinear controller design to steer the process between different operating points. The main features of the controller are that it includes a state observer and dynamic state feedback. The process disturbances are considered in the design as well. The controller is designed for a wide range of nonlinear process dynamics where the performance of a linear controller dramatically deteriorates. The state observer includes a nonlinear state space simulation model of the process being estimated from measured input/output data. The state vector is partitioned into two parts which reflect our a priori knowledge about the process dynamics. The design algorithm is verified using a simulation model of a fluidized bed polymerization reactor. No assumptions are made in the design that would be violated in application of the controller for a real process.

Adaptive servo controller design using a disturbance observer

Abstract: The authors propose an adaptive speed controller with a disturbance observer for a servomotor control system. The overall control system consists of three elements: a forward speed controller; a parameter identifier; and a disturbance observer. The servomotor system, using a two degree-of-freedom concept, can improve the characteristics of closed loop systems by suppressing the disturbance torque. Moreover, the system can be applied to time-varying systems by employing a parameter identifier. The authors show the performance of the proposed controller through experimental results.

Hierarchical feedback controls in two-machine flowshops under uncertainty

Abstract: This paper deals with an optimal control problem of stochastic two-machine flowshops with machines subject to random breakdowns and repairs. Since the sizes of both internal and external buffers are practically finite, the problem is one with state constraints. As the problem is extremely difficult to solve, it can be approximated by a deterministic problem in which the stochastic machines' capacities are replaced by their average capacities when the rates of machine failures and repairs become large. An explicit optimal feedback control for the deterministic problem is obtained based on a "constraint domain approximation" approach. Furthermore, beginning with the solution of the deterministic problem, a feedback control for the stochastic flowshops is constructed, which is proved to be asymptotically optimal with respect to the rate of change in machine states.