PID Controllers, 2nd Edition

Chapter 7.2 - Control Paradigms: Cascade Control

Cascade control can be used when there are several measurement signals and one control variable. It is particularly useful when there are significant dynamics, e.g., long dead times or long time constants, between the control variable and the process variable. Tighter control can then be achieved by using an intermediate measured signal that responds faster to the control signal. Cascade control i s built up by nesting the control loops, as shown in the block diagram in Figure 7.1. The system in this figure has two loops. The inner loop is called the secondary loop; the outer loop is called the primary loop. The Reason

Figure 7.2 Responses to a load disturbance for a system with (full line_ and without (dashed line_ cascade control. The upper diagram shows process output y and the lower diagram shows control signal u.

for this terminology is that the outer loop deals with the primary measured signal. It is also possible to have a cascade control with more nested loops. The performance of a system can be improved with a number of measured signals, up to a certain limit. If all state variables are measured, it is often not worthwhile to introduce other measured variables. In such a case the cascade control is the same as state feedback. We will illustrate the benefits of cascade control by an example.

EXAMPLE 7.1 Valve positioners

Consider the system shown in Figure 7.1. Let the transfer functions be

Assume that a load disturbance enters at the input of the process. There is significant dynamics from the control variable to the primary output. The secondary output does respond much faster than the primary output. Thus, cascade control can be expected to give improvements. With conventional feedback, it is resonable to use a PI controller with the parameters K = 0.37 and T_i= 2.2. These parameters are obtained from the simple tuning rules presented in Chapter 5. The response of the system to a step change in the load disturbance is shown in Figure 7.2.

Since the response of the secondary measured variable to the control signal is quite fast, it is possible to use high loop gains in the secondary loop. If the controller in the inner loop is proportional with gain K_s, the dynamics from setpoint of C_s to process output becomes

This is faster than the open loop dynamics, and higher controller gains can be used in the outer loop. With K_s= 5 in the inner loop and the PI control with K = 0.55 and T_i= 1.9 in the outer loop, the responses shown in Figure 7.2 are obtained. The PI controller parameters are obtained from the simple tuning rules presented in Chapter 5. The figure shows that the disturbance response is improved substantially by using cascade control. Notice in particular that the control variable drops very much faster with cascade control. The main reason for this is the fast inner feedback loop, wich detects the disturbance much faster than the outer loop.

The secondary controller is proportional and the loop gain is 5. A large part of the disturbance is eliminated by the inner loop. The remaining error is eliminated at a slower rate through the action of the outer loop. In this case integral action in the inner loop will always give an overshoot in the disturbance response.

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Chapter 7.2 - Control Paradigms: Cascade Control

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