Robert P. Van Til

Constrained controllability of discrete-time systems†

The constrained controllability of the discrete-time system xk+1=A(k)xk+B(k)u,k is considered where the control uk is termed admissible if it satisfies specified magnitude constraints. Constrained controllability is concerned with the existence of an admissible control which steers the state x to a given target set from a specified initial state Conditions for checking constrained controllability to a given target set from a specified initial state are presented. These conditions involve solving finite-dimensional optimization problems and can be checked via numerical computation. In addition, conditions for checking global constrained controllability to a given target set are presented. A system is globally constrained controllable if for every initial state, there exists an admissible control that steers the system to the target. If a given discrete-time system is constrained controllable, it may be desirable to obtain an admissible control that steers the system to the target from a specified initial s...

Constrained controllability of discrete-time systems with additive disturbances

The constrained controllability of a discrete-time system with additive disturbances is considered where the control and the disturbance are termed admissible if they satisfy specified magnitude constraints. Constrained controllability is concerned with the existence of an admissible control which steers the state of the system to a given target set from a specified initial state for every admissible disturbance. It is shown that the disturbed system is constrained controllable if, and only if, an associated disturbance-free system is constrained controllable. Thus, existing results from the literature concerning the constrained controllability of disturbance-free systems can be used to check the constrained controllability of disturbed systems.

Using a discrete event simulation program in an engineering probability and statistics course

The discrete event simulation software QUEST is being used in a sophomore level engineering probability and statistics course. This course is required for all engineering students in the school. Students learn about the basics of the QUEST operating environment and how to assemble and run simple simulation models. For more complex systems, the students modify and run existing simulation models that have been developed by the instructors. The simulations are used to illustrate the effects of changing the probability distribution of events on the behavior of a system or to generate random data to be used to analyze a systems behavior. Besides being used as a random number generator, the assignments provide the students with an understanding of the nature of system simulation (as opposed to analytical analysis). The QUEST-based laboratory assignments are described and assessment results obtained to date are presented.

Application of discrete-time quantized data controllers to systems with disturbances

In a recent paper, a new method for the digital control of a continuous-time system based on a table look-up technique was presented. This digital controller is called a discrete-time quantized data (DTQD) controller. In order to minimize the number of table entries, a grid embedding process is proposed. This control technique proved successful when applied to the regulator problem. However, when a DTQD controller using the grid embedding process is applied to a continuous-time system with additive disturbances, the performance of the DTQD controller degraded, causing oscillations and possible limit cycle phenomena. In this paper, the grid embedding process is replaced with a continuous scaling process. The continuous scaling process retains the advantages of the grid embedding process in reducing the number of table entries. In addition, it reduces the amount of oscillation in the system response when disturbances are present.

Global constrained holdability of discrete-time systems

Global constrained holdability of a discrete time system is considered. This problem is concerned with determining if for every initial state in a given convex holding set, there exists a control, subject to specified magnitude constraints, which keeps the state of the system in the holding set. A condition for checking global constrained holding is presented. A method for computing a control, subject to specified magnitude constraints, which holds the state of the system in the holding set for a prescribed initial state is also given.

A Novel Method to Reduce Inspection Process Cycle Time While Using a Coordinate Measurement Machine

A touch-based probe of a coordinate measurement machine (CMM) is generally used to validate the dimensions of the artifacts and associated features which come out of the manufacturing line against its dimensions to ensure to be within prescribed GD&T [Wilson 14] limits. Although there could be other applications using a CMM like reverse engineering, however the stated inspection process is quite crucial for maintaining quality factor and to regulate merits of the manufacturing process especially with the continuous wear-tear of the involved tooling. However this inspection process, which is considered as auxiliary process, needs to have minimum cycle time in order to effectively have more quality units to be produced.In this paper we describe Computer Aided Process Planning (CAPP) in order to complete Computer Aided Inspection (CAI) process using CMM on the work-piece which is created through Computer Aided Design (CAD) and Manufacturing (CAM). This leads to Computer Integrated Manufacturing (CIM) process. As a result, the features, which need to be inspected, could be recognized from its corresponding CAD file and appropriate information could be culled out by the Dassault Software System to calculate the approach and retract points to inspect the features [Choudhury 03].The main objective of this research paper is to determine the shortest collision free trajectory from the retract point of one feature being inspected to the approach point of another feature being inspected so that the sequencing for the set of trajectories could be calculated through existing Traveling Sales Person (TSP) algorithm in order to shorten the total distance travelled by the CMM probe, which in turn would linearly reflect in reducing the cycle inspection time. Further since different features in the work-piece might need to be inspected by different probes, an overhead time and displacement for probe change, needs to consider in order to shorten the cycle time. These include clustering of similar type of features, which can be inspected by the same probe. Also clustering of similar type of features need to be assessed against spatial distance of separation between the clusters that the probe has to travel. Since the CMM travels at a constant low speed and the different probes are of similar shape, size and comparatively very small weight, the motion dynamics of the CMM does not influence the total distance travelled for the inspection process.Our main contribution is in the development of a spatial algorithm which not only reduces the inter-feature distance but also does that by avoiding the potential for any collision with the feature or the artifact without the use of any computer vision or collision avoidance sensor information. The resulting spatial algorithm has implicit embedded information of feature clustering, which when fed into an optimization algorithm generates a path planning which would eventually shorten the cycle time. The illustration is done with two separate simulations.Copyright

Analysis of a new signal for bottleneck identification and loss allocation to individual machines

This paper presents a new signal for analysis to identify and rank the bottlenecks in a manufacturing system. The proposed method analyses interdeparture time from different machines to identify and rank the bottlenecks. A simple descriptive measure with good correlation to bottleneck is presented. This research also presents a new method to allocate loss of production to different machines based on the analysis of inter-departure time. In addition, a set of rules that may be used to improve data integrity is presented. The proposed method may be used to analyse both steady-state as well as nonsteady-state system behaviour. The proposed method is applicable to high-volume and low-variety manufacturing systems. Future research issues are discussed.

Procedures for estimating desirable initial states of a production line: a comparative study

Two procedures for estimating initial states of a production line that ensure the line has a high probability of meeting the specified production target during a scheduled production shift are presented. The problem of determining desirable initial states is important in low variety, high volume production systems such as those from the automobile industry. One procedure is derived from design of experiments (DOE) theory whereas the other uses a genetic algorithm (GA). In the study it was determined that both procedures are straightforward to implement and produce good solutions to the problem. The results from the procedures are compared and their benefits and disadvantages are discussed.