Showing papers presented at "American Control Conference in 1993"

Extended Kalman Filter Based Nonlinear Model Predictive Control

Abstract: This paper formulates a nonlinear model predictive control algorithm based on successive linearization. The extended Kalman filter (EKF) technique is used to develop multi-step prediction of future states. The prediction is shown to be optimal under an affine approximation of the discrete state / measurement equations (obtained by integrating the nonlinear ODE model) made at each sampling time. Connections with previously available successive linearization based MPC techniques by Garcia (NLQDMC, 1984) and Gattu & Zafiriou (1992) are made. Potential benefits and shortcomings of the proposed technique are discussed using a bilinear control problem of paper machine.

Delayed Positive Feedback Can Stabilize Oscillatory Systems

Abstract: This paper expands on a method proposed in [1] for stabilizing oscillatory system with positive, delayed feedback. The closed-loop system obtained is shown (using the Nyquist criterion) to be stable for a range of delays.

A New Method for Identifying Orders of Input-Output Models for Nonlinear Dynamic Systems

Abstract: The paper proposes a new method for identifying orders of input-output models for unknown nonlinear dynamic systems. The approach is based on the continuity property of the nonlinear functions which represent input-output models of continuous dynamic systems. The approach does not depend on any nonlinear function approximation methods and solely depends on the system's input-output data measured in experiments. By evaluating the modification of an index which is defined as Lipschitz number with the successive modification of model orders, the appropriate model orders can be determined simply and reliably. Theoretical background of the present approach is discussed. Several examples from chaotic dynamic systems, nonlinear plant models are presented to demonstrate the effectiveness of the present method.

Receding Horizon Recursive State Estimation

Abstract: A discrete time, receding horizon, recursive state estimation scheme based on the batch state estimation least squares formulation is presented. It is shown that this procedure yields the same state estimate as the standard Kalman filter. Nominal stability of a constrained batch state estimation formulation is demonstrated and a constrained, receding horizon, recursive state estimation formulation is presented.

Robust Stability of Constrained Model Predictive Control

Abstract: A new design technique for a robust model predictive controller is proposed using an uncertainty description expressed in the time-domain. Robust stability of the resulting closed-loop system is guaranteed for a set of Finite Impulse Response (FIR) models. Both necessary and sufficient conditions for asymptotic stability are stated. If the uncertainty is described as lower and upper bounds on impulse response coefficients, then the resulting optimization problem can be cast as a linear program of moderate size.

Control of Parametrically-Dependent Linear Systems: A Single Quadratic Lyapunov Approach

Abstract: In this paper two parameter-dependent control problems for linear, parametrically varying (LPV) systems are presented. Sufficient conditions for exponential stability and an induced L 2 -norm performance objective are given. The resulting synthesis problems are reformulated into convex optimization problems which can be solved with efficient new algorithms.

A Robust Adaptive Nonlinear Control Design

Abstract: An adaptive control design procedure for a class of nonlinear systems with both parametric uncertainty and unknown nonlinearities is presented. The unknown nonlinearities lie within some "bounding functions" which are assumed to be partially known. The key assumption is that the uncertain terms satisfy a "triangularity condition." As illustrated by examples, the proposed design procedure expands the class of nonlinear systems for which global adaptive stabilization methods can be applied. The overall adaptive scheme is shown to guarantee global uniform ultimate boundedness.

Control System Analysis and Synthesis via Linear Matrix Inequalities

Abstract: A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are "analytical solutions" to these problems, but in general they can be solved numerically very efficiently. In many cases the inequalities have the form of simultaneous Lyapunov or algebraic Riccati inequalities; such problems can be solved in a time that is comparable to the time required to solve the same number of Lyapunov or Algebraic Riccati equations. Therefore the computational cost of extending current control theory that is based on the solution of algebraic Riccati equations to a theory based on the solution of (multiple, simultaneous) Lyapunov or Riccati inequalities is modest. Examples include: multicriterion LQG, synthesis of linear state feedback for multiple or nonlinear plants ("multi-model control"), optimal transfer matrix realization, norm scaling, synthesis of multipliers for Popov-like analysis of systems with unknown gains, and many others. Full details can be found in the references cited.

Multiple Steady States in Homogeneous Azeotropic Distillation

Abstract: In this article we study multiple steady states in ternary homogeneous azeotropic distillation. We show that in the case of infinite reflux and an infinite number of trays, multiple steady states exist when the distillate flow varies non-monotonically along the continuation path of the bifurcation diagram with the distillate flow as the bifurcation parameter. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the distillation region boundaries. We also locate in the composition triangle the feed compositions that lead to these multiple steady states. We show that the prediction of the existence of multiple steady states in the case of infinite reflux and an infinite number of trays has relevant implications for columns operating at finite reflux and with a finite number of trays. Using numerically constructed bifurcation diagrams for specific examples, we show that these multiplicities tend to vanish for small columns and/or for low reflux flows.

Sensor/Actuator Failure Detection in the VISTA F-16 by Multiple Model Adaptive Estimation

Abstract: Multiple model adaptive estimation (MMAE) is applied to the Variable Inflight Stability Test Aircraft (VISTA) F-16 flight control system at a low dynamic pressure flight condition (0.4M at 20000 ft). Single actuator and sensor failures are first, followed by dual actuator and sensor failures. The system is evaluated for complete or "hard" failures, patial or "soft" failures, and combinations of hard and soft actuator and sensor failures. Residual monitoring is discussed for single and dual failure scenarios. Performance is enhanced by the application of a modified Bayesian form of MMAE, scalar residual monitoring to reduce ambiguities, automatic dithering where advantageous, and purposeful commands.

Dynamic Friction Models and Control Design

Abstract: In this paper we propose two new dynamic friction models that include most of the relevant properties that friction has been observed to have (Stribeck effect, hysteresis behavior, spring-like characteristics in stiction and stick-slip regime). Properties of these models that are relevant to control design are studied. In particular we analyse the dissipative properties of the models. New control strategies are investigated and stability results are presented.

Parametric Uncertainty Modeling using LFTs

Abstract: In this paper a general approach for modelling structured real-valued parametric perturbations is presented. It is based on a decomposition of perturbations into linear fractional transformations (LFTs), and is applicable to rational multi-dimensional (ND) polynomial perturbations of entries in state-space models. Model reduction is used to reduce the size of the uncertainty structure. The procedure will be applied for the uncertainty modelling of an aircraft model depending on altitude and velocity (flight envelope).

Adaptive Observer for Active Automotive Suspensions

Abstract: An adaptive observer for a class of nonlinear systems is developed. Conditions for convergence of state estimates and parameters are presented. The developed theory is used for observer-based parameter identification in the active suspension system of an automobile. The observer uses measurements from two accelerometers and an LVDT. It adapts on dry friction which is usually present in significant magnitudes in hydraulic actuators of active suspensions. Experimental results on a half-car suspension test rig are presented.

Computational complexity of μ calculation

Abstract: The structured singular value μ measures the robustness of uncertain Systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems.

Digital Filter Control of Remotely Operated Flexible Robotic Structures

Abstract: This paper presents an infinite impulse response (IIR) filtering technique for reducing structural vibration in remotely operated robotic systems. The technique uses a discrete filter between the operator's joy stick and the robot controller to alter the inputs of the system so that residual vibration and swing are reduced. A linearized plant model of the system is analyzed in the discrete time domain, and the filter is designed using pole-zero placement in the z-plane. This technique has been successfully applied to a two link flexible arm and a gantry crane with a suspended payload.

Nonlinear Control of a Non-Minimum-Phase CSTR

Abstract: Continuous stirred tank reactors (CSTRs) are central components of many plants in the chemical and biochemical industry. These systems may exhibit highly nonlinear dynamics, especially when consecutive and side reactions are present. In this paper, first an example of a complex reaction system in a CSTR which leads to a nonlinear dynamic behaviour with unstable zero dynamics is described in detail. Then one particular control problem for this system is analysed and solved using a novel combination of gain scheduling and linear frequency domain design techniques.

Optimal Redesign of Linear Systems

Abstract: This paper suggests a redesign procedure for linear systems. We suppose that an initial satisfactory controller which yields the desired performance is given. Then both the plant and the controller are redesigned to minimize the required active control effort. Either the closed loop system matrix or the closed loop covariance of the initial design can be preserved under the redesign. Convex quadratic programming solves this problem. In addition, an iterative approach for integrated plant and controller design is also proposed, which uses the above algorithm in each step. Convergence of this algorithm is also proved. Examples are included to illustrate the procedure.

PID Controller Design for a TITO System

Abstract: This paper presents a new auto-tuning method for designing a diagonal PID controller for a TITO system. From the auto-tuning results a design method is developed based on moving the critical point to a desired position on the compensated characteristic loci. An example is given to illustrate the design method.

Controlling Non-Minimum Phase Nonlinear Systems - The Inverted Pendulum on a Cart Example

Abstract: Control design for minimum phase nonlinear systems has been well developed in the literature via the input-output linearization method developed in [Isi89] and elsewhere. Since a minimum phase system has stable internal dynamics, one may only need to design a control for the linear subsystem after performing input-output linearization for such a system. This paper addresses the design of controls for non-minimum phase nonlinear systems that result in stable output regulation or tracking with acceptable closed-loop performance. The approach is based on the decomposition of a system into an input-output subsystem and an internal dynamics. The developed results are applied to the classical inverted pendulum on a cart example. Simulation and experimental results are reported.

Convergence Rates for Nonholonomic Systems in Power Form

Abstract: This paper investigates the convergence rates of several controllers for low dimenional nonholonomic systems in power form. The method of multiple scales is found to be effective in determining the asymptotic form of the solutions. The general form of the perturbation solutions indicates how parameters in the control laws may be chosen to achieve a desired convergence rate. A detailed analysis of controllers exhibiting exponential convergence is included.

Implementing Modified Command Filtering to Eliminate Multiple Modes of Vibration

Abstract: The requirements for large robots in waste management and space applications necessitate active vibration control algorithms. The use of long, flexible links provides the needed range of motion but their inherent flexibility can generate undesirable vibrations making both control and endpoint positioning difficult. This paper presents two shaping algorithms, the impulse shaping method and the modified command filtering technique, to eliminate the first two modes of vibration in a flexible manipulator. The vibration suppression capabilities are demonstrated using a large elliptic trajectory that produces a significant change in the system properties of the two-link robot. The acceleration response of the tip of the manipulator provides a means of comparison for the different shaping algorithms.

A complete solution to the general H ∞ control problem: LMI existence conditions and state space formulas

Abstract: This paper presents all controllers for the general H∞ control problem (with no assumptions on the plant matrices). Necessary and sufficient conditions for the existence of an H∞ suboptimal controller of any order are given in terms of three Linear Matrix Inequalities (LMIs). Furthermore, we provide the set of all H∞ suboptimal controllers explicitly parametrized in the state space using the positive definite solutions to the LMIs. The inequality formulation converts the existence conditions to a convex feasibility problem, and also a free matrix parameter in the controller formula defines a finite dimensional design space, as opposed to the infinite dimensional space associated with the Q-parametrization.

Robust Digital Tracking Controller Design for High-speed Positioning Systems

Abstract: In this paper, a design approach for robust digital tracking controllers for high-speed positioning is proposed. In high-speed tracking, the combination of a feedforward controller and a robust feedback controller is desirable: the robust feedback controller compensates for mechanical nonlinearities, parameter variation, and disturbances and lets the dynamic behavior of the actual feedback loop system stay close to the nominal one, which makes it possible for the feedforward controller to correctly anticipate and compensate for closed loop dynamics. The idea of disturbance observers is utilized to construct a robust feedback system, and is combined with the idea of zero phase error feedforward controllers. The overall system is demonstrated to possess excellent tracking performance by simulation and experiment.

Connections between the Popov Stability Criterion and Bounds for Real Parameter Uncertainty

Abstract: The purpose of this paper is to investigate an extension of ? theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed ? and absolute stability theory. In particular, it is shown that the upper bounds for mixed ? are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered.

Design of Reliable Controllers Using Redundant Control Elements

Abstract: Design of reliable controllers is proposed utilizing redundant sensor and/or actuators to guarantee H ? norm based performance in case of single outages.

Robustness and Perturbation Analysis of a Class of Nonlinear Systems with Applications to Neural Networks

Abstract: We study robustness properties of a large class of nonlinear systems, by addressing the following question: given a nonlinear system with specified asymptotically stable equilibria, under what conditions will a perturbed model of the system possess asymptotically stable equilibria which are close (in distance) to the asymptotically stable equilibria of the unperturbed system? In arriving at our results, we establish robustness stability results for the perturbed systems considered and we determine conditions which ensure the existence of asymptotically stable equilibria of the perturbed system which are near the asymptotically stable equilibria of the original unperturbed system. These results involve quantitative estimates of the distance between the corresponding equilibrium points of the unperturbed and perturbed systems. We apply the above results in the qualitative analysis of a large class of artificial neural networks.

Input Shaping With Negative Sequences for Reducing Vibrations in Flexible Structures

Abstract: Input shaping by convolving system commands with impulse sequences has been shown to be an effective method of reducing residual vibrations in flexible systems [1, 3, 5, 6, 7]. The three-impulse sequence developed by Singer & Seering [6] extends the move duration by the period of the vibrational frequency while eliminating residual vibrations at that frequency. In Singer & Seering [6], the input shaping sequence is constrained so that frequencies other than the one being shaped are not excited and actuator limits are not exceeded. By carefully relaxing these constraints, we can generate input shaping sequences with move times shorter than those of the three-impulse sequence while providing comparable vibration reduction and insensitivity to modeling errors. This paper presents five different methods for calculating sequences with relaxed constraints. The first two methods permit the excitation of certain frequencies, but maintain the constraint on actuator limits. Both an analytic method and a method of optimizing using non-linear programming are presented. Third, a method is presented which uses the optimization routines to permit exceeding the steady-state actuator limits while staying within peak actuator limits. Fourth, an alternate constraint which enables greater insensitivity to system frequency variations is discussed. Finally, a method for constraining the excitation of specific higher frequencies is presented. The various techniques are demonstrated on a one-link flexible beam.