Lab Proposal for Integrated Real-time and Control - DCS - UPC

More documents

Recommendations

Info

2Fig. 1.Plant and control setup.(a) RCRC circuit(b) Control setupthe plant. Hence, the plant was selected among those for whichan accurate mathematical model could easily be derived.Plants such as an inverted pendulum or a direct currentmotor are the defacto plants for benchmark problems in controlengineering [4]. However, their modelling is not trivial andthe resulting model is often not accurate. This leads to a firstcontroller design that has to be adjusted by ”engineering experience”,thus requiring knowledge that is difficult to formalizeand transmit to the students. To avoid such a kind of drawbacks,a simple electronic circuit in the form of an RCRC(Figure 1a) was selected. The simplicity of its components andtheir simple and intuitive physical behavior have been the mainreasons for its selection. Note however that experiments usingother plants can be complementary to the approach presentedhere, e.g. [2], [5]–[7]. Indeed, Lim [6] also proposes electroniccircuits. However, they are slightly more sophisticated becausethey include operational amplifiers. Although richer dynamicscan be achieved, the intuitive behavior and thus the modelingof operational amplifiers is not straightforward.The selection of an electronic circuit as a plant has alsoanother important advantage: depending on the specific circuit,it can be directly plugged into a micro-controller without usingintermediate electronic components, as shown in Figure 1b,where the zoh box (zero order hold) represents the actuator andthe box above represents the sampler. That is, the transistortransistorlogic (TTL) level signals provided by the microcontrollercan be enough to carry out the control. Notethat this is not the case, for example, for many mechanicalsystems. Such a simplification in terms of hardware reducesthe modelling effort to study the plant and no models foractuators or sensors are required. Additional benefits of thesetypes of plants are that systems can be easily built, are cheap,have light weight, and can be easily transported and powered.The control objective would be to have the circuit outputvoltage V out (controlled variable) to track a reference signal orto settle to a constant value while meeting for example giventransient response specifications, which mandates to use trackingstructures. The control will be achieved by sampling V out ,executing the control algorithm and applying the calculatedcontrol signal to the circuit via varying the circuit input voltageV in (manipulated variable). Disturbances can be injected by avariable load voltage placed in parallel to the output voltage.B. Processing platformThe processing platform consists of the hardware platformand the real-time operating system. As hardware platform,a micro-controller based architecture was selected becauseembedded systems are typically implemented using this typeof hardware. Note, however, that too small micro-controllersmay not be powerful enough for running an RTOS, as discussedin [9]. Among the several possibilities available on themarket [10], it was decided to adopt the Flex board [11].The Flex board (in its full version) represents a good compromisebetween cost, processing power, and programmingflexibility. It was produced as a development board for buildingand testing real-time applications using standard componentsand open source software. The board includes a MicrochipdsPIC DSC micro-controller dsPIC33FJ256MC710, a socketfor the 100 pin Plug-In Module (PIM), an ICD2 (in-circuit debugger)programmer connector, a USB (Universal Serial Bus)connector for direct programming, power supply connectors,a set of leds for monitoring the board, an on-board MicrochipPIC18F2550 micro-controller for integrated programming, anda set of connectors for daughter boards piggybacking.The board has several key benefits that make it suitable tobe used for educational purposes. First has a robust electronicdesign, which is an important feature when it is employedby non skilled users. Second, it has a modular architecture,which allows users to easily develop home-made daughterboards using standards components. A set of daughter boardscan be added to the Flex board for easy development, suchas a multi-bus board equipped with CAN (Controller AreaNetwork), Ethernet, I2C (Inter-Integrated Circuit), and othercommunication protocols. On one hand, the availability ofCAN or Ethernet permits to build and experiment with networkedcontrol applications. On the other hand, the availablenetworks can be used for debugging purposes or for extractingdata from the board, which is a difficult task when dealing withembedded systems.As far as the real-time kernel is concerned, different possibilitieswere considered. First, many well-known real-timeoperating systems, such as real-time Linux [12], target processorsthat may be too powerful for embedded applications. Butmore important, their internal structure is often too complexfor those students with a low profile in (real-time) operatingsystems. Hence, it looks more desirable to work with smallreal-time kernels (see e.g. [13]–[18] for small real-time kernelstargeting small architectures) whose internals are accessible,easy to understand and modify, in order to tailor them to thespecific application needs. On the other hand, from a userpoint of view, programming and configuring the kernel (includingcreating tasks, assigning priorities/periods/deadlines,
3and setting the scheduling policy) should be friendly enoughto attract non-skilled programmers.From the considerations mentioned above, Erika Enterprisereal-time kernel [11] was selected. Erika provides full supportto the Flex board in terms of drivers, libraries, programmingfacilities, and sample applications. The kernel, available underthe General Public License and OSEK (Open Systems andtheir Interfaces for the Electronics in Motor Vehicles, [19])compliant, is a RTOS for small micro-controllers based on anAPI similar to those proposed by the OSEK consortium. Thekernel gives support for preemptive and non-preemptive multitasking,and implements several scheduling algorithms [20].The API provides support for tasks, events, alarms, resources,application modes, semaphores, and error handling. All thesefeatures permits to enforce real-time constraints to applicationtasks to show students the effects of sampling periods, delaysand jitter on control performance.The development environment for Erika Enterprise is basedon cross-compilation, avoiding typical students misconceptionswhen the development platform and the target sharethe same hardware. A tool, named RT-Druid [11] (based onEclipse [21]), can be used as a default development platformto program in C, with support from Microchip for the compilerand for the programming development kit. The latteris important because Microchip web-pages [22] are always agood place where to share experiments experiences and code:a good place for instructors and students to visit. RT-Druid implementsan OIL (OSEK Implementation Language) languagecompiler, which is able to generate the kernel configurationfrom an OIL specification. Apart from programming in C, theFlex board can also be programmed automatically using theScilab/Scicos [23] code generator (similar to what can be donewith MATLAB/Simulink [24] and its Real-Time Workshop, asused for example in [25] for rapid control prototyping). Thisis an important benefit for non-skilled C programmers.From an education point of view, it is also important to notethat there is the possibility to build a community around thisprocessing platform to create a repository of control softwarefor education. In fact, a set of application notes that describe aset of control experiments (inverted pendulum, ball and plate,etc.) developed with Erika on Flex can be found in [11].Finally, it must be stressed that the price of the Flex boardlies in the lower bound of evaluation board prices, and thatthe Erika kernel and the associated development tools areopen source, available for free, or available for free in studentedition format. Hence, it is an economically atractive option.III. EXAMPLE OF THE LAB EXPERIMENTThis section presents some of the activities in the form ofproblems and solutions (and observations) required to carryout the lab experience, which are later ordered in the workplan. The emphasis is in the control analysis and design part.A. Problem 1. Plant modellingIf q i represents the charge on capacitor C i , the differentialequations of the circuit, in terms of the currents ˙q i at each R i ,are given by˙q 1 R 1 +(q 1 −q 2 ) 1 C 1= V in˙q 2 R 2 +(q 2 −q 1 ) 1 1+q 2C 1 C 2= 0 (1)q 21C 2= V out ,For example, using state-space formalism, a state-spaceform is given byẋ(t) =y(t) =[]0 1−1x(t)R 1R 2C 1C 2−[ ]R1C1+R2C2+R1C2R 1R 2C 1C 20(2)+ 1 u(t)[ R 1R] 2C 1C 21 0 x(t)where u(t) is the control signal, y(t) is the plant output, andx(t) = [ x 1 x 2 ] is the state vector, where x 1 correspondsto the output voltage V out , and x 2 is ˙q 2 /C 2 .Observation 1: The modelling of the plant could have beenalso done in terms of a transfer function (see [26] for theanalysis). Even obtaining the differential equations is a goodexercise. Adopting the state space formalism may add anotherbenefit if using model (2). Since only the output voltagex 1 canbe physically measured, the control algorithm requires the useof observers for predicting x 2 . This opens the door to experimentwith several types of observers and the implementationof the controller has to include them. Also, the selection of thestate variables is arbitrary, and therefore, students have to takedesign decisions. For example, the voltages in both capacitorscould also have been chosen as a state variables. In any case,if possible, it is interesting to chose the state variables in sucha way that the controlled variable is directly available throughthe output matrix in order to minimize computations in themicro-controller.B. Problem 2. Electronic componentsThe selection of the electronic components is very importantfor several reasons. The output impedance must be lowenough to properly connect the circuit to the analog-to-digitalconverter (ADC) or to some external instrumentation, suchas an oscilloscope. For example, given the initial componentsR 1 = R 2 = 1 KΩ andC 1 = C 2 = 33µF, a manageable circuitimpedance is obtained. With these components, the state spacemodel becomes[ ] [ ]0 1 0ẋ(t) =x(t)+ u(t)−976.56 −93.75 976.56y(t) = [ 1 0 ] x(t).(3)Observation 2: Students can be given other values. Forexample, with R 1 = R 2 = 330 KΩ and C 1 = C 2 = 100ηF, it is easy to see that the equivalent output impedance istoo high for the ADC. To derive such a conclusion, studentshave to consult the dsPIC data sheet.
Page 1: 1Lab Proposal for Integrated Real-t
Page 6 and 7: 6(a) Fast closed loop response(a) S
Page 8 and 9: 8Fig. 10.(a) Overshoot controller w

Lab Proposal for Integrated Real-time and Control - DCS - UPC

Create successful ePaper yourself

Delete template?

Save as template?