This article is intended for new Linux users who wish to use their Linux-box for some real work. Speed control of an industrial motor? Sounds complicated? It’s not as complex an affair as it sounds. What’s interesting is that a PC powered with a Linux based Real-Time Operating System (RTOS) can be used to control anything from a small motor to a complex industrial drive with the utmost reliability. This article presents the implementation of a Digital PI (Proportional+Integral) Controller on a PC running RTAI (Real Time Application Interface). A system developed on Linux-2.4.24 kernel patched with RTAI-3.1 was used for the speed control of a 12V DC motor.

Control systems

Control systems can be broadly divided into two: open loop systems and closed loop systems. Systems which do not automatically correct the variations in their output are open loop systems. This means that the output is not fed back to the input for correction. For instance, consider a traffic control system where the traffic signals are operated on a time basis. The system will not measure the density of the traffic before giving the signals thereby making it an open loop system.

Consider now a temperature control system, say an air conditioner. The output of this system is the desired room temperature. Obviously, this depends on the time that the supply to heater/cooler remains ON. Depending on the actual temperature sensed by sensors and the desired temperature, corrective measures are taken by the controller. Thus the system automatically corrects any changes in output by monitoring the same; hence, making it a closed loop system.

An open loop system can be modified into a closed loop system by providing a feedback. The provision for feedback automatically corrects the changes in the output due to disturbances. So, the closed loop system is also called an automatic control system. The general block diagram of an automatic control system is shown in figure 1.

Figure 1: Closed system block diagram

Automatic controller

A controller is a device introduced into the system to modify an error signal and to produce the required control signal. An automatic controller compares the actual value of the plant output with the desired value, determines the deviation, and produces a control signal. This will reduce the deviation to zero or to a smaller value. According to the manner in which the controller produces the control signal (called control action), controllers are classified as proportional (P), integral (I), derivative (D) or combinations of these (PI, PD and PID).

The proportional controller is a device that produces a control signal u(t), which is proportional to the input error signal, e(t) (error signal is the difference between the actual value and the desired value) i.e.:

u(t) = Kp * e(t)

where Kp = proportional gain or constant; proportional controller amplifies the error signal by an amount Kp. The drawback of the P-controller is that it leads to a constant steady state error. Integral control is used to reduce the steady state error to zero. This device produces a control signal u(t) which is proportional to the integral of the input error signal:

 
u(t) = Ki * integral { e(t)*dt } 

where Ki = integral gain or constant. Integral control means that we are considering the sum of all errors over an interval. So this always gives us a measure of variation over a constant interval. The other choice is derivative control where the control signal (u(t)) is proportional to the derivative of the input error signal (e(t)). We consider the derivative of e(t) at a given instant as the difference between present and previous errors. A large positive derivative value indicates a rapid change in output variable (here the speed of motor). In other words, the rate of change of speed is more. The drawback in integral controller is that it may lead to oscillatory response. For these reasons combination of P, I and D are used. Most (75-90%) of controllers in current use are PID. In this article, I will look at the design of a PI controller.

The PI controller looks at:

1. the current value of the error; and
2. the integral of the error over a recent time interval.

This not only determines how much correction to apply, but for how long. Each of the above two quantities are multiplied by a “tuning constant” (Kp and Ki respectively) and added together. Depending on the application, one may want a faster convergence speed or a lower overshoot. By adjusting the weighting constants, Kp and Ki, the PI is set to give the most desirable performance. The implementation of software PI controller is discussed later in this article.

Figure 2: A digital PI controller

Today, digital controllers are being used in many large and small-scale control systems, replacing analog controllers. It’s now common practice to implement PI controllers in its digital avatar, which means the controller algorithm is implemented in software rather than in hardware. The trend toward digital control is mainly due to the availability of low-cost digital computers. Moreover, as the complexity of a control system increases, demands for flexibility, adaptability and optimality increases. Digital computers used as compensator are a better option in such cases. A general purpose computer, if used, lends itself to time-shared use of other control functions in the plant.

The systems that ensure timing requirements are termed as real-time systems. An appropriate operating system should be used to satisfy time constraints

Why real-time?

Using general purpose computers is a disadvantage, if the operating system employs various tasks to be executed on a time shared basis. An example of such an operating system is GNU/Linux, where the time constraints required by the control system are not met.

The systems that ensure timing requirements are termed as real-time systems. An appropriate operating system should be used to satisfy time constraints.