Richard W. Longman

Iterative learning control and repetitive control for engineering practice

This paper discusses linear iterative learning and repetitive control, presenting general purpose control laws with only a few parameters to tune. The method of tuning them is straightforward, making tuning easy for the practicing control engineer. The approach can then serve the same function for learning/repetitive control, as PID controllers do in classical control. Anytime one has a controller that is to perform the same tacking command repeatedly, one simply uses such a law to adjust the command given to an existing feedback controller and achieves a substantial decrease in tracking error. Experiments with the method show that decreases by a factor between 100 and 1000 in the RMS tracking error on a commercial robot, performing a high speed trajectory can easily be obtained in 8 to 12 trials for learning. It is shown that in engineering practice, the same design criteria apply to learning control as apply to repetitive control. Although the conditions for stability are very different for the two problems, one must impose a good transient condition, and once such a condition is formulated, it is likely to be the same for both learning and repetitive control.

Identification of observer/Kalman filter Markov parameters - Theory and experiments

This paper discusses an algorithm to compute the Markov parameters of an observer or Kalman filter from experimental input and output data. The Markov parameters can then be used for identification of a state-space representation, with associated Kalman or observer gain, for the purpose of controller design. The algorithm is a nonrecursive matrix version of two recursive algorithms developed in previous works for different purposes, and the relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and offers bounds on the proper choice of observer order. It is shown that if one uses data containing noise and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. The results of the paper are demonstrated in numerical studies and experiments on the Bubble space telescope.

Identification of linear structural systems using earthquake-induced vibration data

This paper addresses the issue of system identification for linear structural systems using earthquake induced time histories of the structural response. The proposed methodology is based on the Eigensystem Realization Algorithm (ERA) and on the Observer/Kalman filter IDentification (OKID) approach to perform identification of structural systems using general input-output data via Markov parameters. The efficiency of the proposed technique is shown by numerical examples for the case of eight-storey building finite element models subjected to earthquake excitation and by the analysis of the data from the dynamic response of the Vincent-Thomas cable suspension bridge (Long Beach, CA) recorded during the Whittier and the North-ridge earthquakes. The effects of noise in the measurements and of inadequate instrumentation are investigated. It is shown that the identified models show excellent agreement with the real systems in predicting the structural response time histories when subjected to earthquake-induced ground motion.

Simple learning control made practical by zero-phase filtering: applications to robotics

Iterative learning control (ILC) applies to control systems that perform the same finite-time tracking command repeatedly. It iteratively adjusts the command from one repetition to the next in order to reduce the tracking error. This creates a two-dimensional (2-D) system, with time step and repetition number as independent variables. The simplest form of ILC uses only one gain times one error in the previous repetition, and can be shown to converge to the zero-tracking error independent of the system dynamics. Hence, it appears very effective from a mathematical perspective. However, in practice, there are unacceptable learning transients. A zero-phase low-pass filter is introduced here to eliminate the worst transients. The main purpose of this paper is to supply a presentation of experiments on a commercial robot that demonstrate the effectiveness of this approach, improving the tracking accuracy of the robot performing a high speed maneuver by a factor of 100 in six repetitions. Experiments using a two-gain ILC reaches this error level in only three iterations. It is suggested that these two simple ILC laws are the equivalent for learning control of proportional and PD control in classical control system design. Thus, what was an impractical approach, becomes practical, easy to apply, and effective.

A mathematical theory of learning control for linear discrete multivariable systems

When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.

A Method for Improving the Dynamic Accuracy of a Robot Performing a Repetitive Task

In many applications it is desirable to improve the dynamic accuracy of robots. In this paper a simple scheme for improv ing the accuracy is presented whereby the robot improves its performance each time the task is performed. The method makes use of the discrete time internal model principle. The performance of the algorithm is confirmed by computer sim ulation studies using a full nonlinear model of a 3-degree-of- freedom robot. The studies indicate that a dramatic improve ment in dynamic accuracy is achievable with the method.

Improvement of Observer/Kalman Filter Identification (OKID) by Residual Whitening

This paper presents a time-domain method to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data. The identified filter has the properties that its residual is minimized in the least squares sense, orthogonal to the time-shifted versions of itself, and to the given input-output data sequence. The connection between the state space model and a particular auto-regressive moving average description of a linear system is made in terms of the Kalman filter and a deadbeat gain matrix. The procedure first identifies the Markov parameters of an observer system, from which a state space model of the system and the filter gain are computed. The developed procedure is shown to improve results obtained by an existing observer/Kalman filter identification method, which is based on an auto-regressive model without the moving average terms. Numerical and experimental results are presented to illustrate the proposed method.

Discrete frequency based learning control for precision motion control

Concerns MIMO learning control design with well behaved transients during the learning process. The method allows dynamic and inverse dynamic control laws. The theory gives a unifying understanding of the stability boundary for convergence to zero tracking error, and of a stability condition obtained by using frequency response arguments. The former is easy to satisfy, making learning control converge with little knowledge of the system. The much more restrictive frequency response condition is interpreted as a robustness condition, representing the robustness relative to good transient behavior during learning. This ensures that the amplitudes of the frequency components of the error signal decay in a monotonic and geometric manner with each successive repetition. Noncausal zero phase filtering is used both to facilitate the generation of learning controllers having this convergence at important frequencies, and to ensure that the learning controllers maintain this property in the presence of unmodeled dynamics. The approach is in discrete time. Experiments are performed on a 7 degree-of-freedom robot, demonstrating the effectiveness of the design process for producing precision motion control.<<ETX>>

Extracting Physical Parameters of Mechanical Models From Identified State-Space Representations

In this study a new solution for the identification of physical parameters of mechanical systems from identified state space formulations is presented. With the proposed approach, the restriction of having a full set of sensors or a full set of actuators for a complete identification is relaxed, and it is shown that a solution can be achieved by utilizing mixed types of information. The methodology is validated through numerical examples, and conceptual comparisons of the proposed methodology with previously presented approaches are also discussed. ©2002 ASME

On the Number and Placement of Actuators for Independent Modal Space Control

A new formulation of independent modal space control is developed to handle the attitude and shape control problem for large flexible spacecraft. The main advantage of this method is that one can obtain an analytical solution for the optimal control law for very high dimensional systems. The fundamental limitation of previous work—the requirement of one actuator for each mode to be controlled—is relaxed in the new formulation. The closed-loop design is obtained while independently assuring stability and the design may be iterated to improve closed-loop performance. The process is shown to be simple and efficient in a realistic numerical example of spacecraft shape and attitude control. The ease of control law generation by this approach is seen to be obtained at the expense of the ability to adjust directly the penalties on the actuator effort. Actuator placement is seen to be of fundamental importance, and methods are developed which are comparatively simple to use and which can determine optimal actuator locations.