Introduction to Control System

Learning Outcome

Upon successful completion of this module, the student will be able to discuss the principles of control systems and compare differing controller terminology.

Enabling Objectives

The student will be able to:

(a) Describe the operation of an on-off controller.

(b) Differentiate between direct-acting and reverse-acting control.

(c) Define the term offset.

(d) State the purpose of integral mode in a controller.

(e) State the purpose of derivative mode in a controller.

(f) Describe the operation of a proportional controller.

INTRODUCTION

There are several variations in the design of control systems, each producing a different form of controller response to any particular error. These differing responses are referred to as control modes. In industry, most control actions fall within one of these four modes:

1. On-off action, sometimes denoted as two-position control, and usually used alone
2. Proportional action
3. Reset, or integral, action
4. Rate, or derivative, action

Certain combinations of these actions or modes are widely used, such as proportional plus integral, or proportional plus integral plus derivative.

CONTROL MODES

The mode of control chosen for a particular process loop will depend upon many factors, such as:

• Economics
• Preciseness of control required.
• Combined response delay of all the components in the loop
• Safety needs of operating personnel and process equipment.

On-Off Control

By definition, on-off control means that the controller output is at either its minimum or its maximum. The controller will never maintain the control valve in an intermediate or throttling position, If recognition of the existence and the direction of the control error is the basic requirement for a controller, it follows that the simplest controller of all is one which responds only to these two aspects of an error. The simplest of all controllers will respond by moving the control valve as soon as an error is sensed, and it will respond in the correct direction. However, this is as far as it will go. The extent of its response will not be related to the size of the error. In fact, whether the error is large or small makes no difference. The simplest controller always moves the control valve stem the same amount, and this means all the way to its wide open or shut position.

On line, an on-off controller will control the process variable, but continuous cycling will occur. For example, in a temperature control system the control valve will close when the temperature goes above the set point (positive error); when the temperature drops below set point, the valve controlling the steam flow to the heat exchanger will open wide. This results in temperature fluctuations and some overshooting of the process variable above the set point, followed by undershooting, which is illustrated in Fig. 1.

Figure 1: Process Variations

The temperature will oscillate about the set point with an amplitude and frequency that is dependent on the capacity and time response of the process. As the process lag approaches zero, the curve will tend to become a straight line; then, the frequency of the control valve open/close cycle will become high. The response curve will remain constant in amplitude and frequency, as long as the load on the system does not change.

Fig. 2 illustrates a pneumatic on-off controller. As the process variable, which in this case is the transmitter output, exceeds the set point pressure, the flapper is moved closer to the nozzle and the controller output increases. Since there is no controller feedback, as explained under transmitter principles, a slight change in the process variable will cause the controller output to go from minimum to maximum or vice versa.

Figure 2: On-Off Controller

Any controller can be converted from direct-acting, where an increase in error signal in a positive direction will result in increased output, to reverse-acting, where an increase in error signal causes decreased output, by interchanging the set point and process variable signals shown in Fig. 2.

During normal operation of the on-off controller, a neutral zone exists in which no control is initiated, as shown in Fig. 3. For example, if the set point is set at 50% of the temperature range, the process variable (temperature) may rise to 50.5% before the control valve is closed by the controller, and the valve may not be opened before the process variable drops to 49.5%. In the neutral zone of 1% width, valve position depends on the direction of change of the process variable.

Figure 3: Controller Neutral Position

Occasionally, the neutral zone is made adjustable, but the error must always change through some small value before control action occurs. Lost motion in the linkage, along with friction in the controller and control valve, win tend to increase the neutral or dead zone.

The following requirements are necessary for on-off control to produce satisfactory results:

• Precise control must be needed.

• The process must have sufficient capacity to allow the control valve to keep up with the measurement cycle.

• Energy inflow is small relative to the energy already existing in the process.

For proper on-off control, the speed of load changes must be fairly slow and the size of load change should be small. Under these conditions, an on-off controller can be applied with reduced installation costs, if variation of the process from the set point will not affect the final product.

On-off control is frequently found in air conditioning, refrigeration, and home heating systems. It is also widely used in safety shutdown systems to protect process equipment or operating staff.

On-off control is almost always the simplest and least expensive form of automatic control. It can be implemented with commercially-available mechanical, pneumatic, or electronic instrumentation.

Proportional Control

With on-off control, the controller output is either at minimum or maximum, and the controller cannot maintain the process variable at the desired condition. By using a proportional controller, the position of the final control element can be maintained anywhere between the two extremes; therefore, a smoother action can be expected.

Proportional-only control is a term usually applied to any type of control system where the absolute value of the position of the control valve is determined by the relationship between the measured variable and the set point. Change in output (corrective action) is proportional to the size of the error signal, or proportional to the deviation from the set point, so there is one and only one position of the final control element for every value of the process variable. Hence the name proportional controller.

Consider a very simple form of level control, as shown in Fig. 4, where a float operates a control valve at the input of the water supply to maintain the level in the tank. Assume the valve is closed when the tank is full, and fully open when the tank level falls to a minimum; also assume that valve opening causes a linear relation with the flow. For example, 25% valve opening causes 25% flow, 50% opening causes 50% flow.

Figure 4: Simple Proportional Control

If the output rate of liquid from the tank is 200 L/min, one can adjust the turnbuckle on the valve linkage until the set point is at 50% of maximum level. With this condition, the input and output flows would be equal. As the discharge rate is increased to 300 L/min the level in the tank drops, causing the float to drop. This, in turn,- increases the input valve opening so that the inflow is equal to the outflow. Now the level will stabilize below the original set point. Similarly, if the discharge rate is reduced to 100 L/min the level will stabilize above the set point. A change in the level (process variable) must take place before the final control element (the valve) can be repositioned. The difference between the set point and the actual value of the process variable is known as offset. Offset is an inherent characteristic of all proportional-only controllers, and may be defined as a sustained error which cannot he eliminated by means of the proportional mode of control, as shown in Fig. 5.

Figure 5: Offset as a Characteristic of Proportional Controllers

If the pivot F in Fig. 4 is moved to the left, so that the ratio of the lever arm AF/FB is decreased, a smaller change in flow will cause the control valve to go from minimum to maximum opening, and the offset will be reduced.

Fig. 6 shows a moment-balance pneumatic proportional controller. It is actually an on-off controller with a negative feedback bellows added.

Figure 6: Moment

For the controller shown in Fig. 6, initial discussions will assume that the pivot point is adjusted so that L1 and L2 are equal; also, the set point and process variable are both adjusted to a minimum value (assume a 20 to 100 kPa range is used), then adjust the force spring so the controller output is at the minimum value of 20 kPa.

When the process variable increases above the set point, the increase in output will bear a linear relationship with the deviation (process variable minus the set point pressure). As the process variable increases to the maximum value of 100 kPa, the controller output will also increase to be at maximum, as shown in Fig. 7; thus an 80 kPa deviation in the process variable will cause the controller output to increase by 80 kPa. With a proportional controller, this deviation is often referred to as the offset.

The output of the controller (V), or the valve position, is directly related to the process variable (PV). When the process variable goes through its full range of values, the controller output does likewise, and the final control element strokes through 100% of possible opening. The percent of the process variable range that causes 100% change in controller output is often called the proportional band.

Figure 7: Controller Output versus Process Variable

In the above example, the proportional band is 100%, because a 100% change of PV will cause a 100% change of V The ratio of change of output (DV) to change of input (DPV) is referred to as the gain (K) of a proportional controller.

Consider what happens if the pivot in Fig. 6 is now adjusted so that L2 /L1=2, and with a 20 kPa set point and PV pressure applied, the spring force is
adjusted so the output is 20 kPa.

Normally, this calibration is not required on an actual controller, but these design features are too complicated to show in a simple sketch. After this adjustment, if the PV input pressure increases above the set point, the PV signal has to increase only to 60 kPa, or 50%, before the output increases to maximum or 100%.

It can be seen that the width of the proportional band or the gain determines the output from the proportional controller, and the amount of valve movement for a given error (the difference between the value of the process variable and the set point). Also, as the gain is increased or the proportional band is made narrower or decreased, the offset of a proportional controller decreases, causing the process to remain closer to the set point.

Consider Fig. 7 with variations in process load. The gain of the controller can be increased only to a certain value beyond which the controller output will start to oscillate like an on-off controller. Any controller with a proportional band of 2% or less may be considered to operate exactly like an on-off controller. In Fig. 4, if the ratio AF/FB is made very small, a disturbance on the water surface can cause the valve to be positioned from the fully closed to the fully open position.

The fact that the proportional band is equal to the percentage change in the process variable (%PV) that causes a 100% change in the controller output (100% V), suggests that the following equation holds true:

Normally, better control of processes is achieved if the controller output is above minimum value when the error is zero, as any final control element such as a valve operates better at about mid-opening. To overcome this effect, a constant spring force, often called manual reset, is imposed by placing an opposing spring opposite to the negative feedback bellows.

When the process variable is at the set point, the clockwise moments will be equal to the counterclockwise moments, so the force provided by the negative feedback bellows must also be equal to the spring force.

The force of the spring can be adjusted to obtain the desired output when the process variable is at the set point, as indicated in Fig. 8.

Figure 8: Proportional Controller

When a proportional controller is used in a process, offset will always exist. As the gain is increased, the offset will decrease; but increasing the gain beyond a certain limit, depending on the process, will cause undesirable oscillation or instability in output and in the value of the process variable. In some processes, offset cannot be tolerated, as it will result in an inferior product. To overcome this problem, the constant spring force, which is actually manually reset, is replaced by automatic reset or integral bellows.

Proportional Plus Reset Control

Integral action, often called reset, is a controller mode that makes a corrective action whose rate of change is proportional to the size of error and the time it lasts. This is accomplished by adding a positive feedback bellows to a proportional controller, which will continue to change the output until the error is eliminated, or until the controller output is at either extreme of its range. This is shown in Fig. 9

Figure 9: Proportional Plus Reset Controller

Assume that a step change is introduced in the proportional plus integral controller shown in Fig. 9, so the process variable (PV) suddenly exceeds the set point. A step change is a vertical rise in PV. The controller output will immediately increase, due to proportional action, by an amount that depends on the gain and the size of error. This will create a pressure differential across the integral restriction valve. As the pressure differential decreases, the increase in force inside the integral bellows causes an increase in output, followed again by an increase in negative feedback, in order to maintain moment balance.

While this integration is occurring, the controller output is increased further than if proportional action were used alone, so that the final control element is moved further, causing the process variable to approach the set point. As the error approaches zero, or the PV approaches the set point, the pressure differential across the integral adjustment valve will also approach zero.

When the PV is at the set point, moment balance is achieved, so that the set point and PV pressures are equal, and likewise the pressure in the negative feedback bellows is equal to the pressure in the integral bellows. If the process variable drops below the set point, the action in the controller becomes reversed.

The capacity tank causes a delay in the integral action by providing a capacitance, and thus providing more stability in control. In proportional plus integral controllers, the offset due to proportional action is eliminated over a period of time.

The rate of change of the corrective output by the integral mode is expressed in terms of the output change due to proportional action alone; also, for any given deviation, the change in proportional controller output will depend on the gain. Integral or reset action is always expressed in terms of the time that it takes for the integral action to reproduce or repeat the output due to proportional action after a step change is introduced. The time that it takes integral action to reproduce the proportional action is known as reset time, expressed in minutes.

Figure 10: Reset Control Action

Integral action can also be expressed in terms of repeats per minute. This is the number of times per minute that the initial proportional action is repeated by integral action.

Reset or integral time can be varied by manipulating the integral adjustment valve. If the valve restriction is increased (assuming PV is above the set point, SP), the pressure in the integral bellows that provides positive feedback will increase more slowly, and the controller output will increase at a lesser rate. If the restriction valve is open wide, the pressures in both feedback bellows will increase almost simultaneously, so the positive feedback will cancel the effects of negative feedback immediately. This will result in a very short reset time, and the output of the controller oscillates like an on-off controller.

The output of a reset (integral) controller varies in accordance with the magnitude of the error signal, the difference between the set point and the controlled variable, and the duration of the error. The term integral originates from the mathematical expression that states that the output of the controller is equal to the time integral of the error signal.

The controller response is illustrated schematically in Fig. 10. Initially, the controlled variable is at the set point value and the system is in equilibrium. At time t, there is a disturbance to the process that changes the controlled variable in the form of a step. This creates a constant error signal in the time period from t1 to t2, which results in the controller output changing at a constant rate in an attempt to eliminate the error signal.

Fig. 10 does not show the controlled variable being brought back to the set point, but this would eventually happen. Basically, the output of this controller will change to any value within the output signal range, to alter the manipulated variable so that the controlled variable is maintained at the set point.

The reset action is adjustable, and it should be noted that the adjustment on a controller might be identified in two different ways:

1. Reset rate in repeats per minute, or the number of times that the error signal is duplicated as a change in the controller output signal within one minute. Electronic controllers have a broad range of adjustment of 0.1 to 100 repeats per minute.
2. Reset time is the time in minutes that is required for the error signal to be duplicated once in the controller output signal.

Fig. 11 illustrates how the gain and reset settings can influence the manner in which the controlled variable is returned to the set point. It is interesting to note that the reaction within the process is almost identical when either the gain or the reset is too high, and it is similar again when these settings are too low.

Figure 11: Proportional Plus Reset Controller Responce

Proportional Plus Reset Plus Rate Control

Rate (derivative) control action is normally used with proportional and reset control modes, but it is shown separately in Fig. 12 to help convey the unique action of this mode of control. Rate action creates a large initial controller output reaction which dissipates with time. Thus, it gives the corrective control action an initial boost, allowing the manipulated variable to change quickly and return the controlled variable to normal or near normal.

The rate adjustment of a controller, which is a measure of how quickly the initial action is removed from the controller output, might range from 0. 1 to 25 minutes.

Rate control is used to counteract the time lags in some processes, such as those involving the transfer of temperature changes. In many processes such as temperature control, there is considerable lag or delay from the time that a change in load or some other disturbance takes place, to the time that the change in the process variable is sensed by any controller. Derivative or rate action, which could not possibly control the process by itself, takes into account the speed at which the variable is deviating from the set point.

Figure 12: Rate Control Action

Fig. 13 illustrates the response of proportional action to a ramp change in the process variable and the controller response when rate action is added. At a certain time, To, the process variable starts to deviate from the set point. In another certain time, T2 (in minutes), proportional action alone will increase the controller output from A to B. If the same controller has rate action added to it at time To, when the process variable starts to deviate from the set point, the rate action will cause a vertical rise in output; then proportional action will cause the controller output to increase steadily, taking the controller only T1, minutes to increase the controller output from A to B.

Rate contribution occurs only when there is a change in rate of error. This change occurs only at time To, because after that the error is changing at a constant rate.

The speed of rate action is known as rate time, TD.

In Fig. 13

TD = T2 - T1

If the process variable starts to deviate from the set point at a faster rate, rate contribution to controller output will increase; also, T1 - T2 will become greater.

Figure 13: Rate Contribution to Controller Output