Fundamentals of cascade control
Sometimes two controllers can do a better job of keeping one process variable where you want it.
When multiple sensors are available for measuring conditions in a controlled process, a cascade control system can often perform better than a traditional single-measurement controller. Consider, for example, the steam-fed water heater shown in the sidebar Heating Water with Cascade Control. In Figure A, a traditional controller is shown measuring the temperature inside the tank and manipulating the steam valve opening to add more or less heat as inflowing water disturbs the tank temperature. This arrangement works well enough if the steam supply and the steam valve are sufficiently consistent to produce another X% change in tank temperature every time the controller calls for another Y% change in the valve opening.
However, several factors could alter the ratio of X to Y or the time required for the tank temperature to change after a control effort. The pressure in the steam supply line could drop while other tanks are drawing down the steam supply they share, in which case the controller would have to open the valve more than Y% in order to achieve the same X% change in tank temperature.
Or, the steam valve could start sticking as friction takes its mechanical toll over time. That would lengthen the time required for the valve to open to the extent called for by the controller and slow the rate at which the tank temperature changes in response to a given control effort.
A better way
A cascade control system could solve both of these problems as shown in Figure B where a second controller has taken over responsibility for manipulating the valve opening based on measurements from a second sensor monitoring the steam flow rate. Instead of dictating how widely the valve should be opened, the first controller now tells the second controller how much heat it wants in terms of a desired steam flow rate.
The second controller then manipulates the valve opening until the steam is flowing at the requested rate. If that rate turns out to be insufficient to produce the desired tank temperature, the first controller can call for a higher flow rate, thereby inducing the second controller to provide more steam and more heat (or vice versa).
That may sound like a convoluted way to achieve the same result as the first controller could achieve on its own, but a cascade control system should be able to provide much faster compensation when the steam flow is disturbed. In the original single-controller arrangement, a drop in the steam supply pressure would first have to lower the tank temperature before the temperature sensor could even notice the disturbance. With the second controller and second sensor on the job, the steam flow rate can be measured and maintained much more quickly and precisely, allowing the first controller to work with the belief that whatever steam flow rate it wants it will in fact get, no matter what happens to the steam pressure.
The second controller can also shield the first controller from deteriorating valve performance. The valve might still slow down as it wears out or gums up, and the second controller might have to work harder as a result, but the first controller would be unaffected as long as the second controller is able to maintain the steam flow rate at the required level.
Without the acceleration afforded by the second controller, the first controller would see the process becoming slower and slower. It might still be able to achieve the desired tank temperature on its own, but unless a perceptive operator notices the effect and re-tunes it to be more aggressive about responding to disturbances in the tank temperature, it too would become slower and slower.
Similarly, the second controller can smooth out any quirks or nonlinearities in the valve's performance, such as an orifice that is harder to close than to open. The second controller might have to struggle a bit to achieve the desired steam flow rate, but if it can do so quickly enough, the first controller will never see the effects of the valve's quirky behavior.
Elements of cascade control
The Cascade Control Block Diagram shows a generic cascade control system with two controllers, two sensors, and one actuator acting on two processes in series. A primary or master controller generates a control effort that serves as the setpoint for a secondary or slave controller. That controller in turn uses the actuator to apply its control effort directly to the secondary process. The secondary process then generates a secondary process variable that serves as the control effort for the primary process.
The geometry of this block diagram defines an inner loop involving the secondary controller and an outer loop involving the primary controller. The inner loop functions like a traditional feedback control system with a setpoint, a process variable, and a controller acting on a process by means of an actuator. The outer loop does the same except that it uses the entire inner loop as its actuator.
In the water heater example, the tank temperature controller would be primary since it defines the setpoint that the steam flow controller is required to achieve. The water in the tank, the tank temperature, the steam, and the steam flow rate would be the primary process, the primary process variable, the secondary process, and the secondary process variable, respectively (refer to the Cascade Control Block Diagram). The valve that the steam flow controller uses to maintain the steam flow rate serves as the actuator which acts directly on the secondary process and indirectly on the primary process.
Naturally, a cascade control system can't solve every feedback control problem, but it can prove advantageous if under the right circumstances:
- The inner loop has influence over the outer loop. The actions of the secondary controller must affect the primary process variable in a predictable and repeatable way or else the primary controller will have no mechanism for influencing its own process.
- The inner loop is faster than the outer loop. The secondary process must react to the secondary controller's efforts at least three or four times faster than the primary process reacts to the primary controller. This allows the secondary controller enough time to compensate for inner loop disturbances before they can affect the primary process.
- The inner loop disturbances are less severe than the outer loop disturbances. Otherwise, the secondary controller will be constantly correcting for disturbances to the secondary process and unable to apply consistent corrective efforts to the primary process.
Steam-fed water heaters as in the example are particularly amenable to cascade control because raising or lowering the steam flow rate raises or lowers the tank temperature without any additional actuators, a valve can manipulate a steam flow rate almost instantaneously in comparison to the slow pace at which steam can heat the water in a large tank, and disturbances to the steam supply pressure are relatively infrequent and easily compensated by the steam flow controller.
Cascade control block diagram
A cascade control system reacts to physical phenomena shown in blue and process data shown in green.
In the water heater example:
- Setpoint - temperature desired for the water in the tank
- Primary controller (master) - measures water temperature in the tank and asks the secondary controller for more or less heat
- Secondary controller (slave) - measures and maintains steam flow rate directly
- Actuator - steam flow valve
- Secondary process - steam in the supply line
- Inner loop disturbances - fluctuations in steam supply pressure
- Primary process - water in the tank
- Outer loop disturbances - fluctuations in the tank temperature due to uncontrolled ambient conditions, especially fluctuations in the inflow temperature
- Secondary process variable - steam flow rate
- Primary process variable - tank water temperature
Cascade control can also have its drawbacks. Most notably, the extra sensor and controller tend to increase the overall equipment costs. Cascade control systems are also more complex than single-measurement controllers, requiring twice as much tuning. Then again, the tuning procedure is fairly straightforward: tune the secondary controller first, then the primary controller using the same tuning tools applicable to single-measurement controllers.
However, if the inner loop tuning is too aggressive and the two processes operate on similar time scales, the two controllers might compete with each other to the point of driving the closed-loop system unstable. Fortunately, this is unlikely if the inner loop is inherently faster than the outer loop or the tuning forces it to be.
And it's not always clear when cascade control will be worth the extra effort and expense. There are several classic examples that typically benefit from cascade control-often involving a flow rate as the secondary process variable-but it's usually easier to predict when a cascade control system won't help than to predict when it will.
Vance VanDoren, PhD, PE, is a Control Engineering contributing content specialist. Reach him at email@example.com.
- When more than one element can affect a single process variable, treating each separately can make the process easier to control.
- One process variable that depends on more than one measurement might need more than one controller.
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