變速箱體左端面鉆孔專用機(jī)床設(shè)計(jì)
變速箱體左端面鉆孔專用機(jī)床設(shè)計(jì),變速,箱體,端面,鉆孔,專用,機(jī)床,設(shè)計(jì)
Decentralized, Modular Real-Time Control
for Machining Applications.
姓名：侍煜煒 專業(yè)班級(jí)：機(jī)械0303
Abstract
Several different architectures for a control system for a reconfigurable machining system are considered, in terms of the inherent delays and their effects on the system performance. It is shown how time delays associated with distributed architectures impact the performance of the control algorithms, and how different types of communication protocols could be implemented to meet the required deadlines. A two-axis contouring system is considered in some detail, and the effects of various delays on the contour error are determined by simulation. These analytic and simulation results can be used to specify the maximum allowable communication delays in the system. Control requirements for a manufacturing control system can thus be mapped to temporal constraints on the data managed for the environment.
1. Introduction
The Engineering Research Center for Reconfigurable Machining Systems at the University of Michigan is developing the necessary theory and technology to enable the next generation of machining systems to be quickly and easily reconfigured in response to changing market demands and new technology innovation. In order to realize the vision of reconfigurable manufacturing systems, the machine tool hardware, as well as the software which controls it, must be constructed in a modular fashion. We envision that each hardware module, be it a single spindle, linear or rotary axis, or a multi-axis grouping, will have its own sensors as well as control hardware and software modules. When a set of modules are grouped together to forma machine, the control task may demand not only certain requirements for individual axes, but also have constraints on the coordination of interacting axes (as in a contouring application). Thus, the axis-level control modules, running on distributed processors with communication over a network, must be coordinated in an appropriate way to ensure that the desired task is completed with the highest possible speed and accuracy. This coordination gives rise to stringent constraints on both the control execution as well as the data communication between control modules.
In order to design and build modular controllers for modular machine tools, the issue of modularity itself must first be examined. It must be understood how different control algorithms should modularized (what is the appropriate granularity) and how they should be combined. In this paper, we assume that the modules are defined according to their purposes: position servo, cross-coupling, process control, etc. We consider the issues of how the control algorithm modules should be allocated among the many processors and how the communication between processors should be scheduled; we also discuss the performance tradeoffs associated with the different choices.
The accuracy of a machine tool is often described in terms of the axis errors and the contour errors (i.e., various deviations from the precisely required trajectories). While in a machining system there are many sources of errors, in this work we focus on the errors associated with realtime, distributed communication and computation. We consider different controller architectures and the impact of these types of errors on the performance of the data and coordination of control system. Therefore, we assume that there are no errors associated with imperfect modeling of the axis motions, and no disturbances such as electrical noise, thermal deformation, or sensor inaccuracies associated with the machine.
The interactions between the control system and the manufacturing environment, involving large quantities of realtime data, need to be managed correctly and efficiently. The states of the machine tools, the sensor readings,
actuator signals, and control variables, together represent the data to be managed. The various manufacturing activities are coordinated in real-time, and in turn, they impose certain consistency and temporal constraints on the managed data. Yet, it is also necessary to allow autonomous executions in the distributed environment to allow for modularity and reconfigurability. There are currently several related real-time control and coordination efforts at varying stages of development and deployment [1, 2, 3, 4, 11]; an overview can be found in [15]. Our research on the software for distributed coordination protocols has identi.ed the coordination constraints in manufacturing systems that need support from a computing system, see [13, 14].
2. Machine tool control structure
Following Koren et al. [8], in this paper we consider three basic types of control modules for a multi-axis machine tool controller: servo, interpolation, and process. First we consider the axis-level controllers, also called servo controllers, which track reference inputs. Servo controller operates in discrete-time with a sampling time of Ts. An interpolator coordinates the axes by decomposing the desired operation motions into individual axis reference commands [7]. In conventional maching operations, the desired feedrate for each motion is stored in the part program. Intelligent machining systems often adjust the feedrate in real-time to increase operation productivity and quality using adaptive process control.
Adaptive or process control can be used to optimize productivity and accuracy [9]. Even though there are numerous types of process control, most of them are implemented by adapting the desired feedrate and/or reference
positions in response to external inputs or disturbances. Adaptive control algorithms may operate at a different sampling time than the servo controls. Because they act by modifying the reference inputs to the servo controller
(either directly or indirectly through the interpolator), this sample time is usually longer than the sample time of the servo controller but is never shorter (it may be the same). In contrast, the computation time associated with an adaptive control algorithm is often longer than that associated with a servo controller. They may also require the knowledge of many sensor inputs (such as positions, forces, temperatures, etc.). This data may be transmitted over a network, causing communication delays which can affect the performance of the adaptive control algorithms.
One particular example that we will consider is a cross-coupled controller, which can improve the contouring accuracy (independent of the tracking accuracy of each axis) in a two-axis machine tool system [6, 12]. It takes as
inputs both the x and y references and sensed positions, and computes the distance between the actual (x, y) position and the desired contour. This difference is used to either compute appropriate control voltages for both the
x and y axes to add to the outputs of the servo controllers, or to send a signal to the interpolator which then modifies the reference values to the servo controllers. Thus, across-coupled controller can be considered either as part
of the servo loop (if its action is to modify the commanded voltages to the motors) or as part of the adaptive process control (if its action is to modify the commanded references to the servos).
The main example that we will use in this paper is a simple two-axis milling machine for contouring applications. We will examine the effects of delays on the performance of a servo and cross-coupled control system; process control algorithms are currently under investigation. In a contouring system, the control performance criterion is given by the contour error, which is defined as the shortest distance from (x, y) to the desired circle. We will use a cross-coupled controller [12] which estimates the contour error and compensates for it using a constant gain.
3. Computing and communication
architectures for control
The performance of a distributed control system is determined not only by the control algorithm but also by the computing and communication architecture with which the algorithm is implemented. Both computation and communication delays occur in a distributed system, and their effects must be considered. In general, a given control algorithm could be implemented in many different ways, with different numbers of processors and different communication networks. In this section, we first consider the sources and locations of time delays in a control system. We then define four different architectures for machine tool control and examine the advantages and disadvantages of each architecture in terms of reconfigurability and expected performance.
The two main sources of delay in a control system are the communication delay associated with sending information over a network, and the computation delay associated with computing control algorithms on a microprocessor. In Figure 1, we have shown a simple block diagram of a
control system and noted several locations where time delays can occur. A delay in between the servo controller and the plant, caused by the computation time needed to compute the control algorithm, is denoted TCP. A sensing delay from the output of the plant back to the servo controller is denoted TPC. A delay between the interpolator and the reference input to the servo controller, due to communication delays, is denoted TRC. In the event
that adaptive process control is contained in the loop, there could be sensing delays to the controller TPA as well as communication and computation delays between the adaptive control block and the interpolator, which are
lumped together as TAR. Even though there will be only one sensor per state, two different delays (TPC and TPA) are shown in Figure 1 to represent the fact that the time required for the sensed data to reach the control blocks depends on both the network and the system architecture. A centralized control architecture is defined as a single block which computes the control commands to all the actuators of the system and has complete knowledge of the state of the entire system. Since a centralized control algorithm has complete knowledge of the system, it has the best possible performance of all the control design architectures. In order to achieve this level of performance, however, the centralized controller must be implemented on a single processor with negligible computation and sensing delays. This is certainly possible for systems with one or two axes, but becomes more difficult for many degree-of-freedom machines. A centralized control architecture is not considered to be reconfigurable.
The other extreme from a centralized architecture is a decoupled architecture, where actuated degree of freedom has its own control block with only local knowledge of the sensed outputs. As the name implies, a decoupled control architecture cannot compensate for coupling among the degrees of freedom. The decoupled structure naturally lends itself to distribution amongst many processors, which can decrease the magnitude of both the communication and computation delays. Because of the minimal
communication and computation delays, a decoupled control architecture can support a small servo-level sampling time, potentially increasing the accuracy of the axis-level positioning. In addition, a decoupled control architecture is easily reconfigured.
A control system is called hierarchical if each axis has its own servo level controller (with only local state knowledge) and there also exists a supervisory controller with knowledge of the state of the entire system. The computation delay of the servo controller is typically small, but the supervisory controller is often more complex and may have a significant computation delay; the communication delay will depend on the location of the sensors in the network. Unlike the centralized architecture, the hierarchical architecture allows the usage of a distributed, multi-processor structure, which can increase the reconfigurability of system significantly.
A control architecture is decentralized if the control block associated with each servo axis (or group of axes) has knowledge of some (or all) remote states (in addition to all local states). There is no ‘supervisory’ control block with global knowledge of the system. Data is communicated between the control blocks over a network. The interpolator still coordinates the many degrees of freedom by sending the desired reference positions over the network. This type of system architecture has the potential to be easily reconfigurable.
The two-axis system under consideration has simple control modules which could easily be implemented on a single processor. However, it is insightful to consider the four different proposed architectures in order to study the communication requirements of the different types of controllers and the effects of communication and computation delays on the control performance. The two extremes are a centralized controller, in which there is no distributed processing, and a decoupled controller, in which there is no communication between the two axes. The decoupled controller is the simplest type of control architecture, consisting only of the two servo-level control modules, but has the worst performance since the contour error is not
considered and thus cannot be compensated. As noted above, the performance of a machine tool control system can be improved by using a cross-coupled controller. The same cross-coupled control algorithm can be implemented in two different ways as shown in Figure 2: as a hierarchical controller, or in a decentralized (but coordinated) manner.
The control structure shown in Figure 2a is considered to be modular as compared to a centralized controller. There is a servo control module for each axis (x and y) in addition to the cross-coupling module. We also consider the cross-coupled controller in a distributed architecture as shown in Figure 2b. The distributed control increases the modularity of the system by having a cross-coupling control module for each axis but does not change the nominal system performance (i.e., the control equations remain unchanged). Different types of time delays will affect the system in each type of architecture; the effects of these delays will be shown in Section 4.3.
4. Effects of communication and computation delays
It is commonly known that delays in a control system tend to decrease performance and can even cause instability. Due to the nonlinearity associated with time delays, it may be difficult or even impossible to solve analytically for the effects of delays. If the system is reconfigured, and the control structure or algorithms change, the analysis should be done again. In this section, we present a combination of simulations and analysis to show how time delays can affect a system’s performance. Time delay tends to increase the maximum error as well as the average error, and may also change the steady state error of system. Certain combinations of time delays can actually result in improved performance over single time delays. We expect that this type of simulation and analytic information will be useful not only in choosing the best type of system architecture, but also in designing the communication protocols that will be used in a recon.gurable machining system (as described in Section 5.).
4.1. Single axis system
For this preliminary study, we have considered a single-axis, single-loop servo system with an interpolator. We analyzed the effects of the time delays shown in Figure 1 when the servo controller is a PI algorithm, the
plant is a second-order motor, and the reference is a ramp function with unit slope. The errors that we present in Figures 3 and 4 are all expressed as compared to the same system without any time delay. As shown in Figure 3,
the effect of the time delay depends not only on the magnitude of the time delay but also on its position in the control loop. The effects of the combination of different types of time delays in the system are shown in Figure 4. Of particular interest is the fact that for this simple system, the errors due to the time delays are additive. Most notably, the positive and negative steady-state errors associated with the reference and sensing delays cancel. This indicates that if one of these types of delays is unavoidably present in the system, the system designer may compensate for it (at least in the steady-state) by intentionally introducing a delay on the other.
4.2. Analytic results
The modified Z-transform [10], an extension of the traditional Z transform, can be used to analyze the closedloop behavior of our example system with time delays. We first consider the different types of communication delays that may be present in a system. The magnitude of the delays will depend not only on the chosen architecture but also on the speed and configuration of the chosen network. Some networks, such as Sercos, have fixed cycle times and deterministic operation; others, such as Ethernet, are fast but can result in varying communication times.
In any type of distributed system architecture (decoupled, hierarchical, or decentralized), the interpolator will send the reference values to the servo controllers over a network, resulting in a time delay. If the time delay to all
servos is the same, then the interpolator may operate in a “l(fā)ook-ahead” fashion to eliminate the resulting errors. More complex compensation may be required when there are differing time delays to different axes, or the time delay may vary due to a nondeterministic network. A communication delay TRC between the interpolator and the servo controller results in a steady state error of ess = Vr TRC for a type I system with a PI servo controller and a ramp reference input with a slope of Vr. If the reference input were a step, then the steady-state error for the same controller and plant system would be zero.
Some or all of the sensed data may also be sent over a network. The minimum achievable sensing delay will depend on the amount of data that needs to be sent over the network, how often the data needs to be sent, as well as the bandwidth of the network. Of course, the network protocols and architecture will also influence the amount of delay. A sensing delay TPC results in a steady state error of ess = .Vr TPC for a type I system with a PI servo controller and a ramp reference input with a slope of Vr. If the reference input were a step, then the steady-state error for the same controller and plant system would be zero. Because the system output is delayed in amount of TPC, the actual output will end up leading the reference, giving a negative error.
We also consider the delays associated with the finite computation time of the digital computer, TCP . This delay depends not only on the complexity of control algorithm but also on the number of tasks a processor must complete during each sampling period. The effects of this delay can be used to determine the number of processors that should be used in the system in order to meet a given error specification. The steady state value of the error
caused by the computation delay is zero for the given system, even though the maximum overshoot error was increased as the magnitude of this delay increased (see Figure 3). In addition, the maximum overshoot error caused
by this delay was less than the error from the communication delays TPC or TCP. Thus, we should choose the control architecture of the system in order to minimize the communication delays as much as possible, even if that means increasing the computation delay by performing many tasks on a single processor.
4.3. Two-axis contouring system
We simulated the cross-coupled controller with a circular reference input and several different control frequencies and communication frequencies. We varied both the frequency of the servo-level controllers Ts as well as the
frequency of the cross
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