Showing papers on "Robust control published in 1994"

A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators

Abstract: In this paper, a robust multi-input/multi-output (MIMO) terminal sliding mode control technique is developed for n-link rigid robotic manipulators. It is shown that an MIMO terminal switching plane variable vector is first defined, and the relationship between the terminal switching plane variable vector and system error dynamics is established. By using the MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators, a robust controller can then be designed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed. It is also shown that the high gain of the terminal sliding mode controllers can be significantly reduced with respect to the one of the linear sliding mode controller where the sampling interval is nonzero. >

A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer

Abstract: A robust stabilization problem for fuzzy systems is discussed in accordance with the definition of stability in the sense of Lyapunov. We consider two design problems: nonrobust controller design and robust controller design. The former is a design problem for fuzzy systems with no premise parameter uncertainty. The latter is a design problem for fuzzy systems with premise parameter uncertainty. To realize two design problems, we derive four stability conditions from a basic stability condition proposed by Tanaka and Sugeno: nonrobust condition, weak nonrobust condition, robust condition, and weak robust condition. We introduce concept of robust stability for fuzzy control systems with premise parameter uncertainty from the weak robust condition. To introduce robust stability, admissible region and variation region, which correspond to stability margin in the ordinary control theory, are defined. Furthermore, we develop a control system for backing up a computer simulated truck-trailer which is nonlinear and unstable. By approximating the truck-trailer by a fuzzy system with premise parameter uncertainty and by using concept of robust stability, we design a fuzzy controller which guarantees stability of the control system under a condition. The simulation results show that the designed fuzzy controller smoothly achieves backing up control of the truck-trailer from all initial positions. >

Robust constrained model predictive control using linear matrix inequalities

Abstract: The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to explicitly deal with model uncertainty. In this paper, the authors address the robustness issue in MPC by directly incorporating the description of plant uncertainty in the MPC problem formulation. The plant uncertainty is expressed in the time-domain by allowing the state-space matrices of the discrete-time plant to be arbitrarily time-varying and belonging to a polytope. The existence of a feedback control law minimizing an upper bound on the infinite horizon objective function and satisfying the input and output constraints is reduced to a convex optimization over linear matrix inequalities (LMIs). It is shown that for the plant uncertainty described by the polytope, the feasible receding horizon state feedback control design is robustly stabilizing.

Optimal guaranteed cost control and filtering for uncertain linear systems

Abstract: The paper presents results on the design of robust state feedback controllers and steady-state robust state estimators for a class of uncertain linear systems with norm bounded uncertainty. The state feedback results extend the linear quadratic regulator to the case in which the underlying system is dependent on uncertain parameters. The state estimation results extend the steady-state Kalman filter to the case in which the underlying system is also uncertain. >

Variable Structure and Lyapunov Control

Abstract: An introduction to sliding mode variable structure control.- An algebraic approach to sliding mode control.- Robust tracking with a sliding mode.- Sliding surface design in the frequency domain.- Sliding mode control in discrete-time and difference systems.- Generalized sliding modes for manifold control of distributed parameter systems.- Digital variable structure control with pseudo-sliding modes.- Robust observer-controller design for linear systems.- Robust stability analysis and controller design with quadratic Lyapunov functions.- Universal controllers: Nonlinear feedback and adaptation.- Lyapunov stabilization of a class of uncertain affine control systems.- The role of morse-Lyapunov functions in the design of nonlinear global feedback dynamics.- Polytopic coverings and robust stability analysis via Lyapunov quadratic forms.- Model-following VSC using an input-output approach.- Combined adaptive and Variable Structure Control.- Variable structure control of nonlinear systems: Experimental case studies.- Applications of VSC in motion control systems.- VSC synthesis of industrial robots.

Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems

Abstract: Solves a finite-horizon partially observed risk-sensitive stochastic optimal control problem for discrete-time nonlinear systems and obtains small noise and small risk limits. The small noise limit is interpreted as a deterministic partially observed dynamic game, and new insights into the optimal solution of such game problems are obtained. Both the risk-sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states, dynamic programming, and associated separated policies. A certainty equivalence principle is also discussed. The authors' results have implications for the nonlinear robust stabilization problem. The small risk limit is a standard partially observed risk-neutral stochastic optimal control problem. >

Robust adaptive and repetitive digital tracking control and application to a hydraulic servo for noncircular machining

Abstract: This paper presents the development of robust digital tracking control algorithms and their real-time implementation on an electrohydraulic servo-actuator for tool positioning in norcircular machining. Robust adaptive feedforward controller for tracking arbitrary signals and robust repetitive controller for tracking periodic signals against disturbances and unmodeled dynamics have been developed. Experimental results are presented to illustrate the control system synthesis procedures and tracking performance

Control system synthesis via bilinear matrix inequalities

Abstract: This paper introduces the bilinear matrix inequality (BMI) as a simple but flexible framework for approaching robust control system synthesis problems. The BMI is an extension of the linear matrix inequality (LMI) approach that has recently been found to be useful in formulating and solving a limited class of robust control problems, including state-feedback and full-order dynamical output feedback /spl Hscr//sup /spl infin// control, /spl mu//k/sub m/ analysis, simultaneous stabilization, gain-scheduling, and so forth. In particular, the BMI formulation is shown to offer the advantage of handling specifications not amenable to the LMI framework such as constraints on controller structure (e.g., decentralized "block-diagonal" control) and on controller order. The BMI formulation also sheds new insight into the properties and limitations of existing robust control algorithms such as the /spl mu//k/sub m/-synthesis, raising questions about the local optimality of the classical DK-iteration.

On a robust nonlinear servomechanism problem

Abstract: A notion of kth-order robust control for the nonlinear servomechanism problem is introduced. A transmission zeros condition is given for the existence of a kth-order robust control law such that, regardless of small parameter perturbations of the plant and control law, the closed-loop system will induce a stable invariant manifold with the error map zero up to kth-order at each point of the manifold. Such a control law incorporates an internal model of up to k subsystems determined by the exosystem. A special case of the result of this paper recovers the well-known linear robust servomechanism result. >

Robust time-optimal control - Frequency domain approach

Abstract: The design of nonrobust and robust time-optimal controllers for linear systems in the frequency domain is presented. The bang-bang profile is represented as the superposition of time-delayed step inputs or the output of a time-delay filter subject to a step input. A parameter optimization problem is formulated to minimize the final time of the maneuver with the constraint that the time-delay filter cancels all of the poles of the system. The issue of robustness to errors in the model is addressed by placing multiple zeros of the time-delay filter at the estimated locations of the poles of the system. The design technique is illustrated on representative models of large space structures, for rest-to-rest, time-optimal, and robust time-optimal maneuvers. Spin-up maneuvers are shown to be special cases of the general formulation. IME-OPTIMAL control of flexible spacecraft is a topic of current interest.1 Many computational approaches and analyses have been presented in the recent literature to deal with the effects of flexibility. Most of these works deal with planar (singleaxis) rest-to-rest maneuvers under two categories: near-minimumtime control and exact-minimum-time control. The first category of methods is based on smooth approximations to minimum-time control for an equivalent rigid body. This class of methods has been shown to be well suited when applied moments or torques are produced by either throttlable thrusters or reaction wheels.2'3 Higher modes of the system are not excited due to the smoothness of the control profile. The second category of methods deals with on-off thrusters directly. Rajan4 formulates the problem including

The unfalsified control concept and learning

Abstract: The "unfalsified control" concept is introduced as a framework for determining control laws whose ability to meet given performance specifications is at least not invalidated (i.e., not falsified) by the experimental data. The concept provides a clear perspective on the nature of learning in a deterministic setting. The approach is "model-free" in the sense that no plant model is required-only plant input-output data. When implemented in real time, the result is an adaptive robust controller which modifies itself whenever a new piece of data invalidates the present controller. A simple design example based on fixed-order LTI controllers and an L/sub 2/-inequality performance criterion is presented. >

Robust Industrial Control Systems: Optimal Design Approach for Polynomial Systems

Abstract: Introduction to optimal robust control scalar LQG optimal control problem and solution scalar H infinity optimal control problem and solution multivariable LQG optimal control problems and solution multivariable H infinity optimal control problem and solution robust control design procedures H2 optimal filtering smoothing and prediction problems H infinity optimal filtering smoothing and prediction problems industrial applications of H infinity optimal control.

Six degree-of-freedom active vibration control using the Stewart platforms

Abstract: Multiple degree-of-freedom (DOF) vibration control systems are essential for precision control of a wide range of Space-borne structures as well as earth-based systems. This paper studies the design and control problems of a class of multiple DOF vibration isolation systems using the concept of a Stewart truss and Stewart platform mechanism. A novel geometric arrangement of a Stewart platform, called the "cubic configuration" is developed and used. A new design and analysis of actuators employing magnetostrictive material Terfenol-D is presented. Robust adaptive filter algorithms for active vibration control are formulated. Prototype hardware for a six degree-of-freedom active vibration isolation system with the "cubic configuration" of the Stewart platform has been implemented and tested. About 30 dB of vibration attenuation is achieved in real-time experiments. >

On the P-type learning control

Abstract: Sufficient conditions for the robustness and convergence of P-type learning control algorithms for a class of time-varying, nonlinear systems are presented. The authors prove the uniform boundedness of the system state and the input control with respect to the existence of errors of initialization, measurement noises, and fluctuations of system dynamics. Furthermore, the system output converges uniformly to the desired one in absence of all disturbances. Finally, specialization of the results to linear systems are presented. >

Reduced order sliding mode control for pneumatic actuator

Abstract: A new position control algorithm, based on sliding mode control, has been developed for a pneumatic cylinder. In the proposed pneumatic system, commercially available two-way on-off solenoid valves have been used. The inherent robustness property of the sliding mode controller makes it easier to select the switching gains of the controller. Moreover, approximate dynamic modeling of the system makes the controller simple. Since in sliding mode control, the states remain on the sliding surface, the motion of the piston is very smooth. This suggests the potential of pneumatic cylinders as actuators for robot manipulators. The controller is hybrid in nature, consisting of an error amplifier, data conversion devices and an 8088 microprocessor along with various digital circuit accessories. Only one feedback device (potentiometer) is used. Velocity is calculated from the sampled position signals. >

Fuzzy model based control: stability, robustness, and performance issues

Abstract: A nonlinear controller based on a fuzzy model of MIMO dynamical systems is described and analyzed. The fuzzy model is based on a set of ARX models that are combined using a fuzzy inference mechanism. The controller is a discrete-time nonlinear decoupler, which is analyzed both for the adaptive and the fixed parameter cases. A detailed stability analysis is carried out, and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty, which may include modeling error and disturbances. In addition, bounds on the asymptotic and transient performance are given. The main assumptions on the system and model are that they must not have strong nonminimum-phase effects, except time-delay, and the unstructured uncertainty must not be too large. A simulation example illustrates some of the properties of the modeling method and model based control structure. >

A method of multivariable predictive control utilizing range control

Abstract: A process control system which includes at least one manipulated variable and at least one controlled variable, provides a method for robust control of a process. Predetermined constraints of the manipulated variables and the controlled variables, and the present values of the manipulated variables are obtained. New values are calculated for the controlled variables for a predetermined number of points in the future, such that the values of the controlled variables are within the predetermined range, thereby obtaining an optimal robustness of the resultant controller. The manipulated variables are also calculated to be within predetermined constraints, and the controlled variables to fall within a predetermined range when controllable. From a plurality of solutions, a most robust solution is selected. Then the manipulated variables are adjusted to cause the process control system to drive the values of the controlled variables to the calculated values.

Robust stability of time-delay systems

Abstract: There are two fundamental results available when we study stability of a polynomial family that is described by convex polytope in the coefficient space: the edge theorem and the theory based on the concept of convex directions. Many known results can be explained with these two results. This paper deals with a generalization of this line of research to the case of quasipolynomials that are entire functions which include both degree of the independent variable and exponential functions. The main objects of the paper are the developing of the concept of convex directions for quasipolynomials and exploiting this concept for construction of testing sets for quasipolynomial families. One of the primary sources of motivation for the class of problems considered in this paper is derived from process control. A typical problem formulation almost always includes a delay element in each subsystem process block. When we interconnect a number of such blocks in a feedback system, the study of robust stability involves quasipolynomials of the sort considered in this paper. >

Performance analysis and improvement in model reference adaptive control

Abstract: The purpose of this paper is to address the issue of performance by using two additional criteria to assess performance in the ideal and nonideal situations. They are the mean square tracking error criterion and the L/sub /spl infin// tracking error bound criterion. We use these criteria to examine the performance of a standard model reference adaptive controller and motivate the design of a modified scheme that can have an arbitrarily improved nominal performance in the ideal case and in the presence of bounded input disturbances. It is shown that for these cases the modified scheme can provide an arbitrarily improved zero-state transient performance and an arbitrary reduction in the size of possible bursts that may occur at steady state. As in every robust control design, the nominal performance has to be traded off with robust stability and therefore the improvement in performance achieved by the proposed scheme is limited by the size of the unmodeled dynamics, as established in the paper. >

Adaptive admittance control: an approach to explicit force control in compliant motion

Abstract: This paper addresses the problem of controlling a manipulator in compliant motion while in contact with an environment having an unknown stiffness Admittance control is used as an explicit force control scheme in which a force setpoint is specified and is tracked by the force compensator Two adaptive PID and PI force compensators are proposed The compensators ensure robust tracking of step force setpoints and rejection of constant disturbances Since the environmental stiffness can typically vary by several orders of magnitude, compensator adaptation is used to ensure a stable and uniform system performance Dynamic simulation results for a 7 DOF Robotics Research arm are presented to demonstrate the efficacy of the proposed admittance control scheme in executing contact tasks >