Showing papers presented at "American Control Conference in 1985"

Optimal Solution of Dynamic Matrix Control with Linear Programing Techniques (LDMC)

Abstract: LDMC is an optimal multivariable control algorithm which combines linear programming method of optimization with the Dynamic Matrix Control. The LP formulation of DMC allows for the optimum calculation of the future moves in L1 sense. In this work 9 claims are reported with respect to this approach. It will be shown how to formulate the claims made into a LP frame work. Some examples are then presented to show the application of LDMC to any complex linear dynamic system.

A Mu-Test for Robustness Analysis of a Real-Parameter Variation Problem

Abstract: A new interconnection structure is constructed for applying ?-tests to the robust stability problem associated with real parameter variations. Some remarks are made concerning the computability of upper bounds for real-?, and an application of the theory to analysis of the lateral axis flight control system of the space shuttle is given.

Modeling and Control of a Refrigerant Evaporator

Abstract: Based on the balance equations for enthalpy, mass and momentum a theoretical model of a refrigerant evaporator has been developed. The distributed parameter process is approximated by several lumped parameter models. The model is completed by equations for the expansion valve, the compressor and the superheater. Various effects, e.g. the random fluctuations of the liquid-dry-out-point can be explained by the model. The dynamic behaviour of the evaporator is investigated as a function of the manipulating signal U EV (position of the expansion valve) and various disturbances (air temperature ? A , condenser pressure P Cd and compressor rotation speed n C ), considering the superheating temperature ? s as control variable and the evaporator performance Q E , which has to be optimized. Two controllers are considered. First, the control behaviour with a conventional thermostatic expansion valve is shown, which often operates unstable. The control performance can be considerably improved by a controller whose structure and parameters are better adapted to the evaporation process. For the experiments a process computer is connected on-line to the process. It will be demonstrated that the efficiency of the evaporator can be increased by at least 5%.

Persistence of Excitation in Linear Systems

Abstract: This paper develops output reachability characterizations of linear finite dimensional systems, so as to translate excitation properties of system inputs to excitation properties of system outputs, states, or associated regression vectors. Such properties are of fundamental concern for convergence of algorithms involving on-line identification, adaptive state estimation, prediction and control. The case of adaptive control is of particular interest since it is desirable that persistence of excitation of associated regression vectors be maintained in the presence of time-varying feedback controllers. Persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties. The theory of the paper suggests modifications to standard adaptive schemes to ensure the required persistence of excitation.

Polymerization Reactor Control

Abstract: The principal difficulties in achieving good control of polymerization reactors are related to inadequate on-line measurement, a lack of understanding of the dynamics of the process, the highly sensitive and nonlinear behavior of these reactors, and the lack of well-developed techniques for the control of nonlinear processes. Some illustrations of these problems and a discussion of potential techniques for overcoming some of these difficulties is provided.

Dynamics of a Closed Chain Manipulator

Abstract: In many manipulator configurations, where the end effector of the manipulator is in contact with a fixed object, a complete mathematical model for the manipulator dynamics should include the effects of the resulting contact force between the end effector and the fixed object. Equations for such a closed chain manipulator are developed, where the end effector constraint is defined by a smooth manifold. These equations are shown to be complete in the sense that the direct dynamics problem and the inverse dynamics problem are well-posed. This formulation suggests a new approach to planning and tracking control for manipulators in a constrained environment.

Experiments in optimal control of a flexible arm

Abstract: ©1985 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

Selection of Near-Minimum Time Geometric Paths for Robotic Manipulators

Abstract: A number of trajectory or path planning algorithms exist for calculating the joint positions, velocities, and torques which will drive a robotic manipulator along a given geometric path in minimum time. However, the time depends upon the geometric path, so the traversal time of the path should be considered again for geometric planning. There are algorithms available for finding minimum distance paths, but even when obstacle avoidance is not an issue minimum (Cartesian) distance is not necessarily equivalent to minimum time. In this paper, we have derived a lower bound on the time required to move a manipulator from one point to another, and determined the form of the path which minimizes this lower bound. As a numerical example, we have applied the path solution to the first three joints of the Bendix PACS arm, a cylindrical robot. This example does indeed demonstrate that the derived approximate solutions require less time than Cartesian straight-line (minimum-distance) paths and joint-interpolated paths, i.e. those paths for which joint positions qi are given by qi = ai + bi?.

Augmented Models for Statistical Fault Isolation in Complex Dynamic Systems

Abstract: The equation error approach to fault isolation implies the statistical testing of balance equation errors. In this paper, some substantial extensions to the existing methodology are proposed, including - generalized linear dynamic models - the concept of statistical isolability - the idea of and an algorithm for model augmenting - fault sensitivity analysis and filtering

Sampling and Decentralized Fixed Modes

Abstract: The effect of sampling on decentralized fixed modes is analyzed. Decentralized fixed modes are classified as being "structured" and "unstructured". It is shown that for almost all sampling intervals the unstructured decentralized fixed modes will no longer exist in a system after the introduction of sampling. This implies that a continuous-time system with unstable decentralized fixed modes may still be stabilized with digital controllers for almost all sampling intervals.

Techniques for Accommodating Control Effector Failures on a Mildly Statically Unstable Airplane

Abstract: Commercial airplanes are becoming increasingly more sophisticated, placing an increasing burden on pilots to detect and resolve the exhaustive set of possible control effector failures. Automatic techniques are needed to either reconfigure an existing control law or restructure a new control law after failure. A discrete control law has been designed for the longitudinal channel of a mildly statically unstable commercial airplane, to track the glideslope during the approach to landing phase of flight. Single effector failures with time delays for failure detection and identification are analyzed for both the reconfigured and restructured control laws, and results are compared with those from previous research using a statically stable airplane. Strategies considered include reconfiguration and restructuring with new flight conditions. Validation of all cases is made using a 6 DOF nonlinear airplane simulation.

Multivariable Control Systems with Saturating Actuators Antireset Windup Strategies

Abstract: This paper contains preliminary, yet promising, results for introducing antireset windup (ARW) properties in multivariable feedback control systems with multiple saturating actuator nonlinearities and integrating action. The ARW method introduces simple nonlinear feedback around the integrators. The multiloop circle criterion is used to derive sufficient conditions for closed-loop stability that employ frequency-domain singular value tests. The improvement in transient response due to the ARW feedback is demonstrated using a 2-input 2-output control system based upon the F-404 jet engine dynamics.

Information Fusion in Distributed Sensor Networks

Abstract: A distributed sensor network (DSN) consists of a set of processing nodes collecting data from sensors. When the nodes communicate, each node fuses the information received from other nodes with the local information to obtain an updated situation assessment. This paper presents fusion results based on a multiple hypothesis approach. The two important problems of hypothesis formation and evaluation are discussed.

The Optimal Projection Equations for Reduced-Order State Estimation

Abstract: First-order necessary conditions for optimal, steady-state, reduced-order state estimation for a linear, time-invariant plant in the presence of correlated disturbance and nonsingular measurement noise are derived in a new and highly simplified form. In contrast to the lone matrix Riccati equation arising in the full-order (Kalman filter) case, the optimal steady-state reduced-order estimator is characterized by three matrix equations (one modified Riccati equation and two modified Lyapunov equations) coupled by a projection whose rank is precisely equal to the order of the estimator and which determines the optimal estimator gains. This coupling is a graphic reminder of the suboptimality of proposed approaches involving either model reduction followed by "full-order" estimator design or full-order estimator design followed by estimator-reduction techniques, The results given here complement recently obtained results which characterize the optimal reduced-order model by means of a pair of coupled modified Lyapunov equations ([7]) and the optimal fixed-order dynamic compensator by means of a coupled system of two modified Riecati equations and two modified Lyapunov equations ([6]).

A Solution to the Inverse Kinematics of Redundant Manipulators

Abstract: A solution to the inverse kinematics is a set of joint coordinates which correspond to a given set of task space coordinates (position and orientation of end effector). For the class of kinematically redundant robots the solution is generically nonunique such that special methods are required for obtaining a solution. The paper presents a new algorithm for solving the inverse kinematics which is based on a modified Newton-Raphson iterative technique. The new algorithm is efficient, converges rapidly, and completely generalizes the solution of the inverse kinematics problem for redundant robots. The method is illustrated by a numerical example.

Joint Probabilistic Data Association in Distributed Sensor Networks

Abstract: A distributed multitarget tracking problem is considered. The Joint Probabilistic Data Association (JPDA) algorithm has been applied successfully for tracking under the multiple-target and clutter environment. However, it assumes a centralized processing architecture in which all the sensors' measurements are transmitted to a single processor and processed. In many applications, however, a set of local processors are present and each processor processes the local sensors' measurements instead of transmitting them to the central processor. The locally processed results are then interchanged and fused together through the communication network. A distributed version of JPDA algorithm which handles the fusion problem from multiple processors is presented.

Tracking and Disturbance Rejection of MIMO Nonlinear Systems with PI Controller

Abstract: We study tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator. Roughly speaking, we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

The Minimum Number of Degrees of Freedom in State Feedback Control

Abstract: A general eigenvalue assignment (EA) control problem for linear multivariable systems is formulated and solved within the framework of parametric eigenstructure assignment. It is shown that EA control is achievable by means of a family of classes of state feedback EA controllers. The number of classes is equal to the number of admissable Jordan forms of the closed-loop system. Each class is characterised by a specific minimum number N of free parameters (degrees of freedom) in the parametric form of the feedback gain matrix. The class of EA controllers with the greatest value of N is specified.

Expert Control

Abstract: The application of expert systems technology is currently being extended to real-time process control. The potential benefit is to allow rapid application of defined expertise to dynamic problems involving hundreds of variables. The system's approach to this requires the consideration of the challenges of real-time inference, in particular the dynamic nature of the domain, the large knowledge base and the requirements for efficient execution.

Nonlinear Compensator Synthesis via Sinusoidal-Input Describing Functions

Abstract: We describe a new nonlinear compensator synthesis approach and illustrate it with an application to a position servo design problem from robotics. The synthesis technique is based on a set of amplitude-dependent sinusoidal-input describing function (SIDF) models of the nonlinear plant. An intermediate step is the design of a linear compensator set based on these models; final synthesis of the nonlinear control system is accomplished by SIDE inversion to determine the required compensator nonlinearities. The major extension in comparison with earlier research is that the compensator so obtained is fully nonlinear; i.e., there is a nonlinear operator associated with each term (proportional, integral, derivative) in the compensator. This approach is capable of treating nonlinear plants of a very general type, with no restrictions as to system order, number of nonlinearities, configuration, or nonlinearity type, and can be extended readily to include other compensator types, e.g., lead/lag. The end result is a closed-loop nonlinear control system that is relatively insensitive to reference input amplitude.

Effective Rigidity of Robot Structures: Analysis and Enhancement

Abstract: Analysis of effective compliance breakdown between various structural subsystems as well as a novel concept of stiffness enhancement for robot manipulators are considered. Compliance breakdown shows a relatively insignificant role of linkage compliance (2-20% of the overall compliance depending on design) as well as domination of the break-down by one component. A combination link concept allows to reduce end-of-arm displacement as well as necessary driving torque, and increase structural natural frequency. Optimization of the combination link is performed for various combinations of joint-link compliances as well as for various preloads.

Some Extensions of Loop Transfer Recovery

Abstract: In this paper, new conditions for regulator loop transfer recovery (LTR) of minimum phase, non-square, left-invertible, full- or reduced-order observer-based multivariable feedback control systems are derived. It is proved that these conditions are satisfied asymptotically by either the full- or the reduced-order Kalman filters that assume fictitious process noise at the input in the design model. These results eliminate the need for artificially squaring a non-square system and extend the theory to reduced-order observer-based LOG designs. The results are illustrated by a numerical example.

Optimal Control of Systems with Hard Control Bounds

Abstract: The numerical solution of the optimal control and trajectory of systems with hard control bounds is considered. A new algorithm, which extends the gradient method [1] to systems with hard control bounds is presented. The algorithm is based on the use of an Adjustable Control-variation Weight (ACW) matrix to enforce the bounds. The application of the algorithm to the minimum-time control of a two-link robot arm is presented as an example.

Adaptive PID Control

Abstract: Conventional PID controllers are used commonly in industry. However, under various circumstances, such as changing process conditions, the PID loop does not necessarily perform in an `optimal' manner, and retuning may then be required. This paper presents a reformulation of the adaptive pole-placement controller such that subject to some conditions and restrictions, it has the structure of a digital PID controller. Various properties of this adaptive PID controller are described and illustrated by simulation examples.

Predictive Controller Design by Principal Components Analysis

Abstract: A new method of designing predictive controllers has been developed that is based on a singular value analysis of the process dynamics. The primary design parameter is the number of principal components of the system generalized inverse to retain in the approximate process inverse used by the controller. The effects of the individual components on closed-loop performance and robustness can be easily calculated. Choices of other controller design parameters have a minimal impact on the results of the new method. Explicit move suppression is not required. The method works particularly well on MIMO processes and tolerates changes in process scaling and output weighting. Application of the method to two distillation column models is illustrated.

Infinity-Norm Optimization with a Stable Controller

Abstract: The stability of a feedback system with an open-loop stable controller is discussed, and an optimality condition in the infinity norm sense is derived in the MIMO case.

A Slow Manifold Approach to Feedback Control of Nonlinear Flexible Systems

Abstract: In this paper we consider the control problem for a class of coupled, second-order singularly perturbed nonlinear dynamical systems. The problem has important application to flexible mechanical systems including robot manipulators with flexible joinra, where the singular perturbation parameter ? is the inverse of the joint stiffness. For this class of systems it is known that the reduced order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear state feedback, but that the full order flexible system is not, in general, linearizable. We utilize the concept of integral manifold to represent the dynamics of the slow subsystem, which reduces to the rigid model as the perturbation parameter tends to zero. We show that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around ? = 0 we show how to approximate the feedback linearizing control to any order in ?. The result is a nonlinear feedback control scheme to "stiffen" the nonlinear flexible system. That is, the behavior of the closed loop flexible system is nearly that of the controlled rigid system.

Development of CMU Direct-Drive Arm II

Abstract: The CMU Direct Drive Arm II (DD II) is the second direct-drive arm designed and constructed at the Robotics Institute, Carnegie Mellon University. It is an electric 6 degree-of-freedom robot, in which all of the joints are of direct drive construction. Featuring high performance Samarium Cobalt magnet brushless DC motors and light weight aluminum construction, the robot has been designed to have a minimum payload of 2.5 Kg with a maximum transit time of 1 second (corresponding to tip speeds of 4 m/sec). High resolution pancake resolvers are mounted directly to the joint shafts for very accurate feedback. Static accuracy is ±0.1 mm. Taking advantage of the dynamic simplicity inherent in direct drive design, the controller is capable of dynamic force compensation in real-time. Such a controller can accurately follow a trajectory at very high speeds. In this paper we discuss the design of this new arm, particularly our solutions to the difficulties of practical implementation of direct drive.