How Cascade Control System Enhances Dynamic Response to Load Changes

The major limitation of a conventional feedback control system is that the correction for disturbances does not start until the process output deviates from the setpoint. Feedforward control provides big improvements in processes with large time constraints or time delays. But, feedforward control requires that the disturbances be measured explicitly and a model must be available for calculating the controller output. By employing a secondary measurement and a secondary feedback controller, the dynamic response to load changes may be greatly enhanced. The secondary measurement point is located so that it recognizes the upset condition sooner than the process output but the disturbances are not necessarily measured. This is the essence of cascade control. It is particularly useful when the disturbances are associated with the manipulated variable or when the actuator exhibits non-linear behavior such as a non-linear valve or the electrodynamics of a motor.

The cascade arrangement (like the one shown in the figure below) is the common standard for the control of electric drive systems. Hypothetically the velocity could be controlled by a simple controller, measuring the velocity error and then giving the motor such a voltage that the velocity is corrected. However, such a controller would be impractical and extremely sophisticated, because it has to take a large number of features into consideration.

With reference to the figure above, the velocity controller G_R1 calculates an output signal that is, the torque required to accelerate the motor to the desired speed. The desired current, I_ref that the motor requires to produce the torque is computed from a mathematical model of the motor. This model has been denoted by a gain K_T which is adequate for DC motors.

The inner loop controls the current that is necessary to produce the torque. The output of the controller G_R2 is a command to the power electronics unit that produces the necessary voltage input to the motor.

Assume we want to calculate the transfer function from the rotor current setpoint I_ref to the rotor current I; the power electronics and the electrical part of the motor are represented by the transfer functions G_A and G_M1 respectively. Note the real system is not linear however we can still demonstrate the quality of this structure.

The transfer function G_I of the inner loop is:

If the gain of G_R2 is large, then the transfer function G₁ will approach one and will also be quite insensitive to variations in the amplifier or motor transfer functions. Non-linear behavior of the motor or amplifier can often be modeled by transfer functions with variable coefficients.

From the output of the velocity controller there are now three rather simple systems in series, gain K_T, the current control loop G_I, where G_I is close to unity, and the mechanical part G_M2 of the motor. Hence we can see that the cascade structure eradicates many of the inherent complexities in the power electronics and motor dynamics.

Furthermore, the current feedback serves another purpose. Because the rotor current has to be limited, the inner loop functions as a current limiter.

The cascade arrangement is also appropriate for the commissioning (first start-up) of the control system. Initially the inner loop is tuned. This tuning doesn’t necessarily have to be changed when the outer loop is tuned. Because the inner loop has simplified the dynamics, tuning of the outer loop is made much easier.

For position control another loop is added outside the velocity loop and the tuning can proceed in similar way.

Cascade control features can be summarized as:

• The output signal of the master (primary) controller serves as a setpoint for the slave (secondary) controller.
• The two feedback loops are nested, with the secondary loop located inside the primary control loop.
• Last but not least, the dynamics of the secondary loop has to be significantly faster than that of the primary loop.

To avoid wind up in the primary controller, you need to know when the secondary controller saturates. In some systems, the primary controller is set to manual mode when the secondary controller saturates. For computer control, you have to consider the execution order of the two regulators.  Due to the different speeds of the control loops, they may have different sampling rates. The sampling rate for the primary control loop may be significantly longer. If the primary regulator is executed first, then it can present an updated setpoint for the secondary controller. Otherwise, the secondary controller may be fed with an unnecessary old setpoint value. Note that the outer loop controller may receive its setpoint from the operator or some predefined value. The output from the primary controller is not sent to the computer output but to the data area where the secondary controller can pick it up as its setpoint value.

Related articles:

• Basic Steps to Consider in Designing a Control System
• Centralised vs. Decentralised Control Systems
• Adaptive Control System
• Proportional-Integral-Derivative (PID) Control Systems
• Position Control System using a Microprocessor-Based Controller