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| 采用DSP技术设计复杂的嵌入式控制系统（续上文） | |||||
作者：admin 文章来源：本站原创 点击数： 更新时间：2004-7-27  |
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The equations derived above express the acceleration, velocity and position of the shear assembly, as a function of the position of the sheet metal (r). As long as the sheet metal moves with a constant velocity, the acceleration , velocity, and position of the shear (r) can be expressed as a function of time by simply multiplying by the constant velocity of the sheet metal (h).. . q(t) = q(r(t)) w(t) = w(r) h a(t) = a(r) h2 However, if the sheet metal velocity changes with time, these equations bec ome more complex... q(t) = q(r(t)) w(t) = w(r) h(t) a(t) = w(r) s(t) + a(r) h(t)2 ...where s(t) is the acceleration of the sheet metal at any given time. Controlling the motion of the shear Up to this point we have focused our attention on the problem of determining the acceleration, velocity, and position profiles needed to turn the shear between cuts. We will now turn our attention to the problem of designing a c ontrol system that will drive the shear's motor to precisely follow these sp ecified profiles. Unless the cut length happens to exactly match the circumference of the shea r assembly, the shear will need to accelerate and then decelerate (or vice v ersa) as it rotates into position for the next cut. As it makes its final ap proach to the sheet metal, its acceleration, its velocity, and its position must all be precisely adjusted, to ensure proper synchronization of its moti on with the sheet metal. In theory, the acceleration, the velocity of the shear will exactly track th e profiles described by the equations above if we simply drive the motor in such a way that it precisely tracks the equation for its position versus tim e. We could use a digital signal processor to compute successive values for the position curve (using the position equation derived above) and a D/A con verter to convert that stream of digital values into a continuous analog ref erence signal, in real time. Unfortunately, motors never have a perfectly linear response. As a result, t heir motion never precisely tracks the position signal used to drive them. S ome of their nonlinearities are proportional to speed. For example, some ene rgy is lost to friction, and the amount of energy loss increases with motor speed. Other nonlinearities are proportional to acceleration. For example, t he inertia of the motor (and its load) prevent the motor from precisely trac king its position signal. This is where our equations for velocity and acceleration can be used to imp lement feed-forward control. A digital signal processor generates velocity a nd acceleration signals (in addition to the position signal) based on the eq uations derived above. These signals are then weighted and summed with the p osition signal, to drive the motor. (See Figure 12) The weighting factors for the velocity and the acceleration signals are adju sted to precisely compensate for nonlinearities in the motor's response, all owing for precise control of the motor. Note: Some of the motor's nonlinearities are not proportional to position, v elocity or acceleration. For example, when a motor is stopped, static fricti on resists any resumption of motion. This makes the low end of the friction vs. velocity curve nonlinear. To compensate for this, a nonlinear transform table can be used (instead of a simple weighting factor) to scale the veloci ty component that gets summed into the drive signal..(See Figure 13). Implementing the Math Since this application did not require an expensive floating point processor , we used a fixed point processor. However, a few complications arose. The m agnitude of the intermediate equation results had to be carefully watched. T he equations shown above may look nice, but they pose a problem, when coded for computation on a fixed point digital signal processor. You can easily ov erflow the accumulators, or to lose the required accuracy, if you don't pay attention to the order in which computations are performed. The equations shown above are shown in the form in which we derived them, by integration. However, to maintain accuracy we had to rearrange these equati ons, to keep intermediate results within manageable limits. We also rearranged the equations to minimize the number of divide operations . A multiply operation can be performed by a digital signal processor in a s ingle instruction cycle, but a divide operation might require dozens of inst ruction cycles. The equations shown here were rewritten with this fact in mi nd, so that only 1 divide operation was needed for each incoming position sa mple (as opposed to 3). Software Implementing the equations for the feed-forward part of the system is a rela tively simple task. The digital signal processor can be thought of as an evo lved microcontroller - one that is very good at math. The software required to run the system can be subdivided into 3 modules: The main program The interrupt service routine from the shear and feeder motors The interrupt service routine from the VMEbus host, which provides the line speed and the cut-length specifications. The main program The main program initially ramps the speed of the feeder and the shear up to the requested line speed. This must be done with caution, so as not to prod uce irregularly cut sheet-metal blanks during a line speed change. In order for this to happen, the feeder motor and the shear motor must not be fed sig nals that request accelerations beyond their capabilities. (Although feed-fo rward control greatly improves the linearity of the motor responses, the mot ors still can't respond accurately to step accelerations.) Each time a fresh position feedback sample is received (via the serial port) the digital signal processor computes new position, velocity, and accelerat ion values, and sends them to the D/A converters, and hence to the servo-amp lifiers of the motors. The motor interrupt service routines The interrupt service routine for the motors is activated each time a fresh position sample is taken. Each sample is delivered to the interrupt service routine as a single word, which contains a position sample from each of the 2 motors. The interrupt service routine separates and preprocesses these sam ples, before passing them on to the main program. This preprocessing is needed because the samples received from each motor in crease linearly (as the shaft of the motor turns) and then drop back to zero , when the motor reaches 360 degrees. Since the control equations use the pr evious samples from the motor to compute derivatives of the motor's motion, the interrupt service routine must notify the main program each time a revol ution is completed. Since the previous sample was at the top of the ramp, an d the current sample is at the bottom, the previous samples must then be "ad justed" to eliminate the discontinuity. Once it completes all of the preprocessing, the interrupt service routine re turns, allowing the main program to compute new position, velocity and accel eration values, using the control equations. The host interrupt service routine The interrupt service routine for the VMEbus host is far less complex than t he motor control interrupt service routine. It simply retrieves the new line speed and/or the new cut length information, and then notifies the main pro gram that there's a change. The main program then accepts the new informatio n and adjusts its position, velocity and acceleration parameters accordingly . Note: A host computer is not really necessary. New line speed and cut-length specifications could be supplied by thumbwheel switches, or by some other s imilar interface. The Processor Because of its specialized hardware architecture, a digital signal processor can do a multiply-accumulate operation in a single cycle. It also exhibits very little interrupt latency time. These characteristics make it ideal for handling the equations required for real-time modeling of dynamic systems. A single digital signal processor can replace several Programmable Logic Con trollers, greatly simplifying the synchronization of the various motors on a n assembly line. The replacement of several subsystems with a single digital -signal-processor-based controller also greatly simplifies the overall archi tecture, reducing costs by 2 orders of magnitude. The DSP56001 One digital signal processor that lends itself well to embedded control is t he DSP56001 from Motorola. This digital signal processor has several feature s that make it particularly attractive as a real-time processor: Significant internal RAM space (3 Kbytes) Built in Sine and Cosine tables, which are useful if Fast Fourier Transforms (FFTs) and filters will be implemented. Two 56-bit-wide arithmetic accumulators Two 48-bit-wide logical accumulators Seven address registers, complete with offset registers and address mode con trol registers. Addressing may be performed with pre/post increment & decrem ent, indexed by an offset, or bit-reversed (which is useful for working with FFTs). Three separate address spaces - 1 for program and 2 for data. The 2 data spa ces are handy if a signal has a real and imaginary component. Both data spac es can be accessed simultaneously, if necessary Hardware multiply accumulate (single-cycle) Extremely low interrupt latency time - 4 instruction cycles to get to the in terrupt service routine. While some of these features (such as Fast Fourier Transform capability) wer e not crucial for our real-time control application, we found the hardware m ultiply/accumulate and the low interrupt latency time extremely valuable. Th e large internal RAM also allowed us to quickly access heavily used function s and variables. This improved our program execution speed considerably. We used a DSP56001-based processor board from Spectrum. Its 27 MHz processor executes one instruction in 77 nsecs, and it has plenty of external RAM, an d EPROM boot capability. The board is also equipped with serial ports and pa rallel ports. Choosing a hardware platform In addition to the digital signal processor architecture, there are also som e other practical concerns, such as the system architecture that will be pro vided around the chip. The flexibility of the VMEbus architecture (in additi on to its wide variety of analog I/O and motor controller boards) makes it a logical choice. By assembling the system from off-the-shelf boards, we were able to avoid a lot of hardware debugging. In addition, many of these speci alized I/O boards are available in single-height versions, permitting the co nstruction of a very compact VMEbus-based control system. Providing for software development You will probably want to write your software in C. In order to do that you' ll need a C compiler, and an assembler/linker. Motorola provides a GNU C com piler, a simulator, and an assembler/linker that runs on an IBM PC, or on a Sun SPARCstation. We developed our source code on a Sun SPARCstation, and pr oduced an executable code module, which we then downloaded into the digital signal processor for final debug. Spectrum provides a debugging environment that can be run from a PC (interfacing to the DSP board via a serial port) o r over the VMEbus. I/O The analog I/O boards that we used were single-height, off-the-shelf boards from Spectrum. They were 16-bit, dual-channel boards, capable of a 200 KHz A /D sampling rate, and a 500 KHz D/A output rate. We received line speed and cut length specifications from the host computer, through one of the digital signal processor's serial ports. The Prototype We built a small-scale prototype of a flying shear to demonstrate the operat ion of the flying shear controller. (See Figure 14) This prototype system us es a 2 KHz A/D sample rate. If higher accuracy is required, the sample rate can be increased by reprogramming a control register. However, unless higher -resolution shaft encoders are provided on the motors, no benefit will be re alized. The prototype system used Spectron Microsystems' mSpox real-time operating s ystem (running on the DSP56001), as well as Wind River Systems' VxWorks (run ning on a Motorola 68030-based VMEbus host board). The software was developed using STI's N!Power, running on a SPARCstation. S oftware running on the workstation provided a real-time display of the error signals. This workstation was not required to run the system, but was provi ded primarily for display and debugging purposes. Summaryurier Transform capability) were not crucial for our real-time contro l application, we found the hardware multiply/accumulate and the low interru pt latency time extremely valuable. The large internal RAM also allowed us t o quickly access heavily used functions and variables. This improved our pro gram execution speed considerably. We used a DSP56001-based processor board from Spectrum. Its 27 MHz processor executes one instruction in 77 nsecs, and it has plenty of al signal proces sing technology to build high-performance real-time control systems. Complet e families of digital signal processor boards with "real world" I/O capabili ties are now available, off-the-shelf, from VMEbus board suppliers. These VM Ebus boards, as well as off-the-shelf software development tools, allow the prototyping and implementing of real-time embedded control systems, with lit tle or no hardware development. ---------------------------------------------------------------------------- ---- Lawrence Johnson is the applications engineer responsible for VMEbus and SBu s products at Spectrum Signal Processing. He has 3 years experience developi ng hardware and software applications for digital signal processors. Lawrenc e's experience includes the design of ISA cards for audio work, and the writ ing of software for speech compression, graphics processing, and control sys tems. Tim Marchant is the VMEbus and SBus manager at Spectrum Signal Processing. H e has 14 years experience developing and building industrial and ruggedized embedded systems. Tim's experience includes the construction of automation s ystems, data acquisition systems, vehicle monitoring systems, as well as tel ephony applications. |
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