Abstract

This work presents an implementation of a digital PID (Proportional+ Integral+Differential) controller in a PC machine running RTAI. PID controllers are well known and have a wide range of applications in the control of analog systems such as servomotors. In order to achieve the desired performance the system output (axis position) is feed-back to the PID controller which generates… the system input (motor voltage), in a closed loop. The controller computes the error between the desired system output (reference) and the actual system output. Then, the system input, which is the PID controller output, is generated as weighted sum of the error, its integral and its differential. The weighting coefficients are known as controller gains and referred as Kp, Ki, and Kd. The values of the controller gains determines the performance of the closed loop system and even its stability. The design of PID controllers is outside the scope of this paper, however it should be said that its values are very dependent on the sampling rate at which system output is read and the new value for system input generated. Therefore it is highly desirable to have an accurate sampling rate. For typical mechanical systems, the adequate sampling rate is in the range of milliseconds. Thus, well implemented PID controllers are usually hard real time systems. The PID controller described in this work uses the PC parallel port as an analog I/O interface. Just two bits are used. One to read the system output and the other to generate the system input. As the system input and output are analog variables, a technique called Pulse Width Modulation (PWM) is used to generate (and read) analog values using digital signals. This technique is based on varying the duty cycle of a rectangular wave accordingly to the analog value to be represented. By using PWM, an analog interface can be built without the use of conventional A/D and D/A converters. However, the switching rate of the PWM signal should be fast enough to be filtered by the system under control. For typical mechanical systems that means a few hundreds of microseconds. The implemented system can be characterized by four main tasks: Two PWM tasks which generate the input and output signals, a PID task responsible for the controller in a proper sense and a user interface task. Except for the user interface task, each one of the main tasks has its own time requirements which must be accurately met. The user interface was implemented as a plain Linux process using the NCurses library. Real time tasks were provided by threads under LXRT hard real time mode. The implementation of PWM under RTAI using the timing functions provided by RTAI are presented and the convenience of using these functions for actual real time control is discussed. In Particular, the semantics of rt_sleep() is analyzed in details and it is shown that the current semantics can lead to an confusing interpretation of what a periodic task is and what a task period is. Furthermore the current semantics of rt_sleep() is incompatible with the the semantics of rt_busy_sleep(), which can lead to even more confusion. A new semantics for rt_sleep() is suggested and the corresponding implementation presented.

Read full paper (PDF download)

 
This article was originally published on LinuxDevices.com and has been donated to the open source community by QuinStreet Inc. Please visit LinuxToday.com for up-to-date news and articles about Linux and open source.