The software developed for DC motor speed control system provides the user interface to

Transcription

1 5.1 Introduction The software developed for DC motor speed control system provides the user interface to enter the set point, tune controller parameters by using the Matrix type keypad and display the P,PI, and PID logic controller parameter values and key variables like measured speed, set point speed in RPM etc., on Liquid Crystal Display. The complete software is divided into three major parts viz., Measurement, Control and Display. Besides the three major tasks of measurement, control and display, the software first declares and initializes all program variables, constants, and functions. The software then enters the measurement control programs and display them. In measurement, the software acquires the voltage proportional to the speed of the DC motor through A/D converter, substitutes it into the liner equation of the curve between frequency and voltage to find the frequency and hence the actual speed in RPM, and displays it on the LCD. On other hand in control, the software computes the error and change-in-error and applies them to one of the control algorithms P, PI, and PID to generate the control action. Since control action is a digital value, the software sends through D/A converter to get it converted to analog voltage to enable outside world understand the analog signal as the actuating signal for final control element. 121

2 The following section describes the software development for Proportional [P], Proportional plus Integral[PI], and Proportional plus Integral plus Derivate[PID] logics for DC motor speed control system and implementation of P, PI, and PID logic controllers in C language in detail. The necessary algorithm, flowchart and C language programs, software features and C-cross compiler are presented and thoroughly discussed. 5.2 C -Language Cross Compilers In the present market there are a number of cross compilers available like Keil s-ide, Silicon-Laboratory IDE, Cygnal IDE and Ride-IDE etc. The developed tools allow the user to efficiently develop and debug application code. The C programming language and standard libraries are altered or enhanced to address the peculiarities of an embedded target processor. The C programming language is a general-purpose programming language that provides code efficiency elements of structured programming and a rich set of operations. Its generality combined with its absence of restrictions, makes C a convenient and effective programming solution for a wide variety of software tasks. Many applications can be solved more easily and efficiently with C than with other more specialized languages. The compiler offers a number of control directives, which are used to control compilation. Directivities are composed of one or more letters or digits and, unless otherwise specified, can be specified after the filename on the command line or within a source file. 122

3 The program consists of all control directives such as Symbols, Code, and Debug. The DEBUG directive instructs the compiler to include debugging information in the object file. By default debugging, information is excluded from the generated object file. Debug information is necessary for the symbolic testing of programs. This information contains both global and local variable definition and their addresses, as well as function names and their line numbers. Debug information contained in each object module remains valid through the link/locate procedure. This information may be used by the p Vision2 debugger or by any of the Intel-compatible emulators. In the present study, Keil and Si-Lab IDE compilers are used to develop C code for D.C motor speed control. The two C- compilers are optimizing C compiler, which is a complete implementation of the American National standard institute (ANSI) standard for the C language. The Keil and Si-Lab is a ground-up implementation dedicated to generating extremely fast and compact code for the 8051 Microcontroller. The Si-Lab.IDE supports lx, 2x, 3x and 4x Cygnal Microcontrollers and Keil IDE p version is used for simulation purpose. The Keil IDE simulation supports the microcontrollers such as Atmel, Philips, Motorola, Dolphin, Cygnal, Analog devices, Maxim, and Intel etc. 5.3 Experimental Implementation The experimental implementation of the three controllers such as P, PI and PID logic speed controllers for DC motor is accomplished by developing the necessary software for the hardware. The control algorithms are realized on Cygnal Microcontroller using C language in C-cross compiler Si-Lab IDE. The following discussion epitomizes the 123

4 design methodology of P, PI and PID logic controllers for fhe proposed system. The controller provides the reasonable tracking of the motor speed to a pre-specified reference speed [1]. The sensing optocupler and D.C motor arranged properly and it is interfaced with Cygnal microcontroller. The microcontroller acquires the voltage proportional to the speed of the motor through built-in 12-bit A/D converter and substitutes in a wellcalibrated equation to evaluate the actual speed of the motor. The frequency versus voltage (acquired by the Microcontroller) plot is fitted to the following linear equation using MATLAB [2]. Frequency= (vl )/( ) where vl is the voltage acquired by the microcontroller. From the above equation, the speed in RPM is calculated as follows, Speed = (Frequency *1/P)*60 RPM where P represents the number of pluses per one rotation of disk. After evaluation of the speed, the Cygnal microcontroller determines the error (reference speed - measured speed) and change in error (present error - previous error), and applies to P, PI and PID control algorithms. The necessary variables are used in CTanguage to calculate the error and implementing P, PI, and PID logics with the help of Silicon Laboratory IDE C-cross compiler. 124

5 5.3. a. Design of P, PI, and PID speed controllers The basics of the P, PI, and PID controller are already discussed in chapter 1. The designing of mathematical expression for P, PI, and PID controls is presented below Proportional control [P] The most common controller action used in process control is one or a combination of continuous controller modes. In these modes, the output of the controller changes smoothly in response to the error or rate of changes of error. The natural extension of this concept is the proportional mode, where a smooth, linear relationship exists between the controller output and the error. Thus, over some range of error about the set point, each value of error has a unique value of controller output in one-to-one correspondence. The Proportional mode is expressed by P=Kpep where ep= en-e.i Kp=proportional gain ep= error (set point value-measured value) Vn ~ Vn-l + Kp (e - en-i) where, Kp is proportional constant Vn_i is the previous control action en, en.i are the present and previous errors respectively 125

6 Proportional plus Integral [PI] In the proportional mode error occurs because the controller cannot adapt to changing external conditions i.e. changing loads. In other words, the zero error output is a fixed value. The integral mode eliminates this problem by allowing the controller to adapt to changing external conditions by changing the zero-error output. The need for integral action is to it is correct the proportional error as the error does not go to zero in time. PI is a combination of the proportional mode and the integral mode, the analytical expression of PI is P=Kp[ep + Ki 1 epdt] Vn = V _i + Kp (e - e -i) + IQ en T where, Kp, and Kj are proportional, and integral constants Vn.i is the previous control action en, e,,.] are the present and previous errors respectively cycle time T is equal to 1 Proportional plus Integral plus Derivate [PID] One of the most powerful controller operation which combines the proportional, integral and derivate mode. This system can be used for virtually for any process condition. The analytical expression of PID logic for speed control is P=Kp[ep+Kjepdt + K,! dep/dt] 126

7 The well known the mathematical expression for the velocity type PID controller is given as [3-7], Vn= Vn-1 + Kp (e,, - e 4) + K; e T+ Kd/T [(en - 2en.i + en-2)] The above equation representing the velocity algorithm is modified into improved PID difference equation by using trapezoidal rule and interpolation technique that is given by the following equation. V = Vn., + Kp (en - Cn-i) + Ki (e + enj)/2t + K4/6T [(e - 2en_, - 6en.2 + 2en.3 + 2e d)] where, Kp, Kj and Kj are proportional, integral and derivative constants respectively Vn.i is the previous control action e, en-i are the present and previous errors respectively en-2, en-3, and en-4 are previous to previous errors In the present application, the best-tuned Kp, Kj, and Kd values are found to be equal to 68.8, 0.41, and 5.0 respectively and cycle time T is equal to Flowchart of the Proportional Program [P] The flowchart is so drawn that it is self-explanatory and gives the complete idea of how computer sequentially does the different steps involved in measurement and control. The flowchart of Cygnal Microcontroller based Proportional control for DC motor speed control system is shown in Fig to and Fig

8 START Fig Flowchart of the Cygnal Microcontroller based Proportional [P] logic for DC motor speed control system 128

9 (a) (c) Fig A/D conversion (b) P computation and (c) D/A conversion routines 129

10 START i Initialization of all variables and function ofuarto, 12-bit ADC, 12-bit DAC and system clock Displayed set point, P, I values On LCD User enters to set point speed, Kp and press the Start key Read the current speed of D.C motor from F/V converter through 12 A/D converter......i... Computing the speed in RPM Frequency = (vl )/( ) Speed = (Frequency* 60)/12 in RPM and speed value stored in to memory 1 r Compute the error (en= set-point spee d - measured) 'r Fig Flowchart of the Cygnal Microcontroller based Proportional plus integral Program [PI] for logic DC motor speed control system 130

11 (a) (c) Fig A/D conversion (b) PI computation and (c) D/A conversion routines 131

12 START Fig Flowchart of the Cygnal Microcontroller based Proportional plus Integral plus Derivative Program [PIDJ for logic DC motor speed control system 132

13 (a) (c) Fig A/D conversion (b) PID computation and (c) D/A conversion routines 133

14 5.5 Pseudo code The following steps are involved in the controlling of D.C motor speed 1. All the parameters P or Kp and speed of the D.C motor are displayed on LCD. 2. Press Enter or SET function key after the user enters the SP (set point of the D.C motor speed in RPM), and control variables (Kp,Ki and Kd). After entering into the each value pressing Set, then the value is stored into the corresponding variable 3. Otherwise default values are stored in the corresponding variables. 4. The motor is not run until Start key is pressed. 5. The present speed voltage is read with the help of built-in 12-bit DAC, external F/V converter, and opto-coupler in the digital format. 6. The speed value is applied into the frequency equation, then frequency is converted to Speed in RPM unit and stored into the RAM memory and the error is computed and control action (P or PI or PID) is performed. 7. The calculated action (error correction) value is sent through built-in ADC and external PWM and Darlington pair, etc. 8. Again the 5th step to 7th step is repeated until the set time is reached (counter) 9. The speed data is stored in RAM memory and is sent to Personal Computer to investigate the speed performance for control action in graphical format. 10. The first step (main program) is repeated again and the cycle continued. 134

15 References [1] M. S. Mostafa, M. A. EI-Bardini, S. M. Sharaf, and M. M. Sharaf, Fuzzy neural networks for identification and control of dc drive systems, in Proc. of IEEE Int. Conf. on Control Applications, pp , [2] William J. Palm, Introduction to MATLAB 7 for Engineers, McGraw-Hill, New York, 2nd ed., [3] Neil Munro, The systematic design of PID controllers, IEE Colloquium of Symbolic Computation for Control, pp ,17 June [4] K. J. Astrom and T. Hagglund, Automatic Tuning of PID Controllers, in: The Control Handbook, Ed. W. S. Levine, IEEE Press, pp , [5] Ibrahim Kaya, Nusret Tan, and Derek P. Atherton, A simple procedure for improving performance of PID controllers, IEEE Proceedings on Int. Conf. on Control Applications, vol. 2, pp , [6] Jose L.. Tong and James P. Bobis, A model for designing digital PID controllers, IEEE Proc., pp , [7] Nusret Tan, Ibrahim Kaya, and Derek P. Atherton, Computation of stabilizing PI and PID controllers, IEEE Proc. of Int. Conf. on Control Applications, vol, 2, pp , June [8] P. Bhaskar, Parvathi C.S., L. Shrimanth Sudheer, and A. B. Kulkami, Computer based DC micromotor speed control system, J. Instrum. Soc. India, vol. 34, no. 4, pp ,

16 [9] Jose L. Tong and James P. Bobis, A model for designing digital PID controllers, IEEE Proc., pp ,1992. [10] Farzan Rashidi', Mehran Rashidi: and Arash Hashemi-Hoseinit, Speed Regulation of DC Motors Using Intelligent Controllers, IEEE, pp ,2003. [11] Y. S. Ettomi, S. B. M. Noor, S. M.'Bashi and M. k. Hassan, Micro Controller Based AdjustableClosed-Loop DC Motor Speed Controller,IEEE, pp