11 research outputs found
An Analysis and Improvement of the Predictive Control Integrating Component
integrator wind-up and, therefore, it is recommended that separate weighting be used with a modified integrating component predictive controller. The separate weighting also improves the designers intuition with respect to tuning the controller, significantly reducing the time required to generate desired closed loop responses. References Clarke, D. W., and Mohtadi, C, 1987, "Properties of Generalized Predictive Control," World Congress IFAC, Munich. Cutler, C. R., and Ramaker, B. L., 1979, "Dynamic Matrix Control-A Computer Control Algorithm," A.I.Ch.E., 86th National Meeting, Apr. Kurfess, T. R., Whitney, D. E., and Brown, M. L., 1988, "Verification of a Dynamic Grinding Model," ASME JOURNAL OF DYNAMIC SYSTEMS, MEAS-UREMENT, AND CONTROL, Dec., Vol. 110, Kurfess, T. R., 1989 "Predictive Control of a Robotic Weld Bead Grinding System," Ph.D. thesis, MIT Department of Mechanical Engineering. Kurfess, T. R., and Whitney, D. E., 1989, "Predictive Control of a Robotic Grinding System," Proceedings of the NMTBA Eastern Manufacturing Technology Conference, Hartford, CT, Oct. Kurfess, T. R., Whitney, D. E., 1989, "An Analysis and Improvement of the Predictive Control Integrating Component," ASME JOURNAL OF DYNAMIC SYS-TEMS, MEASUREMENT, AND CONTROL, submitted Dec. Kwakernaak, H., and Sivan, R., 1972 Introduction The usefulness of observers for real-time state estimation of linear dynamic systems based on measured system outputs is well known. Procedures for designing observers Another approach to robust state estimation has centered upon the fact that the estimated state is often used for feedback control. Hence, the criterion for observer design in these cases is to reduce the effect of modeling errors on the controlled system response. The work of The current work on robust state estimation using observers is motivated by the need to estimate pressure and temperature fields in thermoplastic injection molding processes, based on a few measurement locations in the mold cavity. Robustness of the estimate to errors in the process model is essential for this application given the complexity of the process. The initial use of the estimated pressure and temperature fields is for more effective process monitoring rather than for feedback control. The robustness of the state estimates obtained using observers, in the presence of system modeling error, is examined in this paper following the procedure of Determination of State Estimation Error Bound • Consider the linear time-invariant system described by x{t)=Ax(t) + Bu(t) y(t)=Cx(t) (1) subject to the initial condition x(0) = x 0 where A, B, and C are (nxn), (nxp), and (mxn) matrices, respectively, and x(t), u{t), and y(t) are («xl), (pxl) and (m x 1) vectors, respectively. A full order observer is designed Copyright © 1993 by ASME based on this model to estimate the state x(t). The observer is described by x(t) =AJt(t) +B c u(t)+L(y(t) -y(t)) y(t)=Cx(t) (2) subject to the initial condition Note that modeling errors are permitted only in the A and B matrices and not in the C matrix. Let the estimation error be defined by Manipulation of subject to the initial condition e(0) = x(0)-x(0) = e 0 (5) The eigenvalues of the augmented system described by (1) and (4) are those of A and F c . We assume that the input u{f) is bounded in magnitude and that all the eigenvalues of A have negative real parts, thus ensuring that the estimation error is bounded if all the eigenvalues of F c also have negative real parts. The solution of where M being the modal matrix corresponding to F c and A a diagonal matrix with the eigenvalues of F c as the diagonal elements. Extension of the results obtained here to the case of repeated eigenvalues is relatively straightforward. Taking norms of both sides of Eq. (6), we get C[ being the real part of the observer pole farthest to the right in the complex plane, assumed to be negative here. Id represents the Euclidean norm of any (n x 1) vector v and IIP! represents the spectral norm of any (n x ri) matrix P above. Also, k(M) is the condition number of the (n x ri) matrix M and is equal to IIMII. HAT 1 ! Note that the expression within curly brackets on the right hand side of Eq. (7) depends on the observer eigenvalues and not on the eigenvectors associates with these eigenvalues. The dependence of the state estimation error bound on these eigenvectors is solely via the condition number k(M) of the modal matrix corresponding to F c . Therefore, for competing observer designs with the same eigenvalues, the only difference is in the modal matrix M. The other terms within the curly brackets would be identical for such competing designs. Equation The result obtained here that the eigenvectors corresponding to the observer eigenvalues be chosen to be as nearly mutually orthogonal as possible to reduce the norm of the state estimation error seems to be a natural extension of a result obtained by The suggested observer design guideline does not address the issue of observer eigenvalue selection despite the fact that eigenvalue selection affects the estimation error. Thus, selection of observer eigenvalues without reference to consequences for estimation error may well lead to more robust observer designs being overlooked. Futhermore, Eq. (7) provides only a bound on the estimation error norm. Therefore, it is possible that even if two observer designs differ only in their eigenvector selections, the actual state estimation error norm may in some cases be lower for the design which yields a higher value of k(M) and hence of the error bound. This is less likely to occur, however, if the difference in the values of k(M) for the competing designs is large. Finally, the results obtained here are valid only for cases where the C matrix is known exactly. The procedure for eigenvector selection and observer gain computation follows that of D'Azzo and Houpis (1988). Since the eigenvectors and reciprocal eigenvectors of a matrix are known to be mutually orthogonal, the procedure begins with selection of the reciprocal eigenvectors of F c to be as nearly orthogonal as possible and normalized to have Euclidean norms of unity. S(\ i ) = (A c T -\ i IC T ) for the n specified eigenvalues of F c . At this point in the observer design, the available freedom in eigenvector assignment is used to obtain as nearly mutually orthogonal a set of reciprocal eigenvectors as is possible. The observer gain matrix is then given by Example of Observer Design Consider one dimensional heat conduction in a bar insulated at both ends, governed by the equation where c is the thermal diffusivity of the bar and u(r, t) is the temperature at the location r and time t. It is assumed here that two temperature sensors are located on the bar, one at each end. Using the two measurements provided by the sensors, we need to estimate the temperature distribution in the bar. It is also assumed that the initial temperature distribution in the bar may be unknown. A third order lumped parameter approximation of the distributed parameter system is developed using the modal expansion method. This lumped parameter model is described in a normalized form by The elements of x are the normalized weighting factors on the responses of the corresponding modes, c' is a normalized version of c. It is assumed that the actual value of c' is 0.11, while for observer design, a value of 0.09 is assumed, indicating about 18 percent error. The elements of the C matrix depend only on the boundary conditions and the form of the partial differential Eq. and yields a condition number of the modal matrix of F c , after equilibration, of 3.43. In design 2, the reciprocal eigenvectors are chosen to get a poorer condition number of the modal matrix of F c , equal to 31.44. The observer gain matrix for this design is given by It should be noted here, as an indication of the restricted nature of the results of There is no guarantee, however, that the norm of the state estimation error will always be lower if the observer is designed as indicated here. In fact, if the initial state estimation error vector is dominated by one component, or if the errors in some of the parameters of the A and B matrices are dominant over the others, the relationship between the state estimation error norms may not be the same as the relationship between the error bounds indicated by Eq. Conclusions In this paper, we have derived an expression for an upper bound on the norm of the estimation error for an observer, in the presence of errors in the system A and B matrices and in the estimated initial conditions. It is shown that, in designing observers for multi-output systems using eigenstructure assignment, if the eigenvectors of the F c matrix are chosen to be as nearly mutually orthogonal as possible, a smaller bound on the state estimation error is obtained and thus may lead to more accurate state estimation. This is demonstrated by means of an example. The approach presented seems most appropriate in the absence of any a priori information on the initial state or the nature of the modeling errors. References Introduction This paper is concerned with the problem of identifying the input-output relationship of an unknown nonlinear dynamical system. Classical adaptive control of deterministic linear systems whose state variables are not all observed makes use of the separation principle (Narendra and Annaswamy, 1989) which says, in effect, that the problems of constructing an observer and parameter estimator can be considered separately. When the system is not observable it is not possible to construct an observer to recover the full state. Furthermore, when the system is nonlinear the separation principle no longer applies, and hence conventional adaptive identification and control techniques offer little hope of effective control of partially observed nonlinear systems. In this paper we show that these difficulties can be avoided by using neural networks instead. Neural networks are already successfully applied in control theory and system identification. In a recent paper, Narandra and Parthasarathy (1990) formalized a unified approach to solving nonlinear identification and control problems using multilayered neural networks. Chen (1990) applied multilayer neural network to nonlinear self-tuning tracking problems. Chu et al. (1990) implemented a Hopfield network on identifying time-varying linear systems. Various learning architectures for training neural net controller are outlined in Psaltis et al. (1988) and some interesting applications of neural networks in adaptive control can be found in Goldenthal an
Rechnergestützter Entwurf -CAD- und Implementierung schneller und robuster Antriebsregelungen für Industrieroboter
Aus der Literatur sind zahlreiche anspruchsvolle Regelungsalgorithmen für Industrieroboter bekannt, die unter akademischen Laborbedingungen ausgezeichnete Ergebnisse liefern. Die Mehrheit der marktüblichen Robotersteuerungen bevorzugen jedoch eher einfache, konservative Regelungskonzepte. Die Hauptgründe für die Nichtakzeptanz sind die hohen Inbetriebnahmekosten, die aufwendigen Hardwareanforderungen sowie die unbefriedigende Robustheit gegenüber Schwankungen oder Unsicherheiten der Modellparameter. Für zukünftige Anwendungen in CIM-Systemen werden jedoch in zunehmendem Maße eine bessere Regelgüte, hohe Robustheit in rauher Industrieumgebung, einfachere Entwurf- und Inbetriebnahmemethoden mit PC-Unterstützung sowie Implementierbarkeit auf preisgünstiger gängiger Mikrorechnerhardware gefordert. Die in diesem Beitrag vorgestellte prädiktive PFC-Regelung stellt ein sinnvolles Alternativkonzept dar, das den genannten Anforderungen optimal gerecht werden kann. Das PFC-Regelungskonzept wurde für einen konventionellen Industrieroboter des Typs Kuka 160 realisiert. Anhand verschiedener experimenteller Untersuchungen sowie eines Benchmarktestes wird die Überlegenheit des PFC-Regelungskonzepts gegenüber der konventionellen PI-Regelung nachgewiesen. (IITB
Smart neuro-fuzzy based control of a rotary hammer drill
In order to reach optimal drill penetration using a rotary hammer, it is necessary to control the two variables, rotational speed and strike rate, of the rotary hammer in such a way that by applying minimal guidance and recoil power, a maximum drill penetration rate can be achieved in the rock. An optimal drill penetration rate is attained through using a given combination of rotational speed and strike rate. Changes in the drill diameter and/or material hardness lead to a false adjustment of the system which has to be re-optimized by an intelligent re-adjustment of the two servo-controlled drives. To achieve a flexible and automatic adaptation of rotational speed and strike rate of the rotary hammer to different material and tool types, an adaptive multisensor drive control based on a self-learning neurofuzzy component has been developed by IITB in cooperation with an industrial partner
Intelligente Regelung eines Bohrhammers mit Neuro-Fuzzy-Methoden
Um mit einem Bohrhammer einen optimalen Bohrverlauf zu erzielen, ist es notwendig, die beiden Stellgrößen Drehzahl des Bohrers und Schlagzahl des Hammerwerkes so zu steuern, dass mit minimaler Führungs- und Rückschlagkraft eine maximale Bohrgeschwindigkeit im Gesteinsloch erzielt wird. Bei einer bestimmten Kombination von Drehzahl und Schlagzahl wird jeweils ein Optimum bezüglich der Bohrgeschwindigkeit erreicht. Änderungen des Bohrerdurchmessers und der Materialhärte ergeben eine Verstimmung dieses Systems, die durch intelligentes Nachstellen der beiden Servoantriebe jeweils nachoptimiert werden muss. Zur flexiblen und automatischen Anpassung der Schlag- und Drehzahl des Bohrhammers an veränderte Material- und Werkzeugtypen wurde am IITB in Kooperation mit einem Industriepartner eine adaptive Neuro-Fuzzy-basierte multisensorielle Antriebsregelung entwickelt und prototypisch realisiert
On the application of a new method for fast and robust position control of industrial robots
There are numerous sophisticated control algorithms for industrial robots (IR) providing perfect results under academic laboratory conditions. The vast majority of IR-control systems on the market prefer rather simple conservative concepts. The main reasons for non-acceptance in practice are the high set-up costs, expensive hardware requirements and poor robustness with respect to parameter variations and model uncertainties. However, sophisticated manufacturing problems of the future (CIM) require model and more a better control performance, a high robustness within a crude industrial environment, more straight forward design and implementation procedures with PC assistance and implementation even on low-price conventional micro hardware. Predictive Functional Control (PFC) represents a new alternative concept for IR-control which can meet the above requirements. In this paper will be reported about the practical application of PFC for the position control of a conventional IR (KUKA 1 60). The excellent control behavior and robustness will be demonstrated by experimental results and a benchmark test. (IITB
Erfahrungen bei der Realisierung eines neuartigen prädiktiven Regelungskonzeptes für Industrieroboter
Die zukuenftigen Aufgaben bei der flexiblen Fertigungsautomatisierung (CIM) setzen neue Massstaebe hinsichtlich der Regelungsguete von Industrierobotern, denen die gegenwaertig verwendeten Regelungskonzepte nicht mehr gerecht werden koennen. In einem gemeinsamen Projekt des IITB mit dem franzoesischen Forschungsinstitut ADERSA wurde ein neuartiges praediktives Regelungsverfahren fuer Industrieroboter entwickelt - Predictive Functional Control (PFC)-, das sowohl den zukuenftigen gehobeneren Leistungsanforderungen der industriellen Praxis gerecht wird als auch mit vertretbarem Aufwand realisiert werden kann. Die wesentlichen Merkmale dieses neuen Regelungskonzeptes und erste experimentelle durch Simulation gewonnene Ergebnisse wurden von den Autoren bereits vorgestellt. In diesem Beitrag soll ueber die weiterfuehrenden Arbeiten zur Realisierung des Regelungskonzeptes auf einer marktgaengigen Steuerung fuer einen Industrieroboter des Typs Kuka 160 berichtet werden. (IITB