Hybrid Control Conversion


by
A H Ahmad Kamil
Information Systems Engineering II
a.kamil@ic.ac.uk

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Abstract


This article will discuss the possibility of converting a logic-only control system to be a hybrid control system. A simple water level control of a tank is used as an example. Relative advantages (or disadvantages) are outlined due to this conversion. The important question may be "WHY is it this conversion needed in the first place anyway?".



Contents


  1. Introduction
  2. Overview of Logical and Continuous Control Systems
  3. Water Level Control of a Tank
      3.1 Using A Logic Control System
  4. The Conversion
      4.1 Overview of the System
      4.2 How It Works
      4.3 Obtaining The Function
  5. A Brief Comparison
  6. Conclusion
  7. References

1. Introduction


Control systems can be categorised according to the type of the signal they processed. Continuous-time control system process only continuous signals (analogue). Discrete, or logical, control systems process only samples data or boolean logic. A hybrid control systems can process both types of signals. Nowadays computer machines are used to implement control systems. For simplification of the article, let assume that there exists a virtual machine which is defined by a particular programming language. The language provides the programmer a collection of primitive notion that supports both continuous-time functions and logical functions. Using this machine together with an appropriate example, the rest of the article will discuss the possibility of converting a logic-based control systems into a hybrid control system.

2. Overview of Logical and Continuous Control Systems


A logical control system is simply governed by the "IF (condition) THEN (action) " statement. A particular action will happen depending on the conditions of the system at a certain instant in time. Continuous-time control system is defined by a continuous function which is differentiable and/or integrable. Anyway, a logic control system has one major disadvantage that is only limited conditions are allowed. If there are too many conditions or rules to be applied then the virtual machine has to make a search in its database to find the corresponding action that has to be taken. It is obviously time consuming and for a system that requires immediate action(s), the delay in the search process may be fatal. On the other hand, logical control is easy to be implemented using Boolean logic, very reliable and economical.

A continuous-time control system is nevertheless quite difficult to be implemented and relatively not that reliable if compare to a logic control system since the components used are more complex. Despite these difficulties, a continuous-time control system is indeed necessary in a few particular area. Temperature control of a nuclear reactor is a typical example.

It therefore does make sense if efforts have been done in developing a control system that can process both logical and continuous-time signals, i.e. a Hybrid control system. An example of controlling the water level of a tank will demonstrate the possibility of converting a logic control system into a hybrid control system.


3. Water Level Control of a Tank


Consider a huge tank that requires the level of the water to be controlled. The tank supplies water to many users and hence the level changes indeterministically. A pipe from the main water supply supplies additional water that is required. Initially a logic control system is applied to maintain the water level at the appropriate level. After a few modification, the conversion into a hybrid control system is demonstrated.


3.1 Using A Logic Control System


The level of the water is controlled using 4 main components namely

Figure 1 shows the control system


Figure 1

Sensor 1, Sensor 2 and Sensor 3 are similar type of sensors that detect whether the water reached level 1, 2 or 3 respectively or not. The rules applied in controlling the water level are simple. The basic principle is that the degree (in X o ) of the opening of the tap is controlled depending on the current water level that is detected by the three sensors. The tap will be opened at the maximum angle (say 270o) when Sensor 3 is being detected. Similarly, the angle will be, say, 90o if Sensor 2 is being detected and the tap will be closed, i.e. X = 0o, when Sensor 1 is being detected. The whole control system is clearer through the pseudo-code programmed in the virtual machine as listed below;


	If Sensor 1 Then X = 0
	else If Sensor 2 Then X = 90
	else If Sensor 3 Then X = 270
	End If
where all sensors are considered to be able to produce a boolean logic which is True if it detects the water and False otherwise.

Additional rules may to be added if necessary especially in a system which requires a more effective control. Anyway, too many rules may cause a huge problem as mentioned earlier. The rules are stored in the virtual machine's database and again, if the rules are huge in size, the action required for a particular condition at an instant in time may be too late and may cause a devastating result. Hence a technique has to be applied to convert the logic-only control system to become hybrid.

4. The Conversion


4.1 Overview of the System


Recall the previous system. Figure 2 shows how it has been modified to become a hybrid control system.

Figure 2

Instead of using three or more sensors of a similar type, only 2 sensors are used that are different in type. Sensor A detects the water level, a logical control component, and Sensor B measures the speed of the water level drops, V (in ms-2), and it is the continuous-time control component. The working principle is simple. The speed measured will determine what is the angle for the tap to be opened using a continuous function. It is the responsibility of the programmer to provide such function. Steps in obtaining the function will be explained later. For this system, a suitable example for the function would be as in figure 3.



Figure 3

From figure 3, we can see that the function is just a straight line. The angle is then linearly proportional to the speed V.

4.2 How It Works


Initially, the water level is at A (refer to figure 2). At this moment, only Sensor A is switched on for energy consumption. The main purpose is to maintain the level of the water at level A. If the level drops, the Sensor A will switch on Sensor B that will measure the speed of the water drops. The value measured will be applied into the function to obtain the appropriate opening angle for the tap. Hence, the water increases.

If the level remains constant but still below level A, then from figure 3, the tap is still open with the minimum angle of, say, 25o. Please note that

  1. Sensor A has the upper hand to Sensor B. i.e. Sensor A will switch off Sensor B if level A is reached and
  2. The level of the water is assumed will not reach below level B.
The pseudo-code for the function is as below;

   LOOP
	IF NOT Sensor A THEN
	   DO X = f(V) UNTIL interrupted by Sensor A
	END IF
   FOREVER

Since the system uses both logical (as in IF ... THEN ) and continuous (as in DO .. UNTIL .. ) signals, the control system is hybrid.

4.3 Obtaining The Function


This is basically the task for the programmer. To obtain a correct function, all the rules are listed and then plotted on the graph. From the graph, these rules can be represented as a simple continuous function. For a better function, the logical rules have to be huge in size and virtually cover every possible condition.

In the above example, the programmer may have to use data obtained by the tester(s) of the system. The virtual machine is then programmed to meet the requirements set earlier. The virtual machine, in addition, has one major advantage to be used in the control system in the given example in the sense that if the tank used has different dimensions then all the programmer need to do is to reprogramme the machine.

5. A Brief Comparison


For a logical control system, it is easy to be implemented, cheap and very reliable. The system just depends on few sensors of similar type and these sensors are unlikely to have a failure. Though sufficient for the given example, different systems need more rules to be added to the controller's database. The response time is therefore increased quite distinctively.

On the other hand, the concept on how the hybrid control system, in the given example, works is straight forward, i.e. measure the speed and change the angle of the tap accordingly. The example uses only two sensors of different types. Anyway, there is a possibility that Sensor B (refer to figure 2) will measure incorrect speed and hence cause different effects. Furthermore, it is relatively costly to implement it since generally Sensor B is more expensive than Sensor A and the system is relatively unreliable.


6. Conclusion


With reference to only one given example, a logic-only control system can be converted into a hybrid control system. The key step is to obtain a continuous function that represents all the logic rules. The programmer for the control machine is responsible in ensuring that the function can be applied and does works in processing continuous signals. This conversion anyway do have relative disadvantages.


7. References