9.3 Nonlinear Controller Elements

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9.3 Nonlinear Controller Elements

The controller design procedures I described in Chapters 2 and 4 through 7 focused primarily on the development of linear control systems. In Chapter 2, I also addressed the benefits of providing a nonlinear element in a system subject to actuator saturation. The nonlinear element in that case was a switch that reduced the integrator windup in a PID controller during periods of large error in the response. Another type of nonlinearity is the limiting of variable magnitudes to prevent overflow in fixed-point computations, as I discussed in Chapter 8 self-test questions 8 through 10.

A limiter is a common element in control system designs that simply limits its output to specified minimum and maximum values. When the limiter's input signal is between the minimum and maximum values, it is passed unchanged. A limiter is useful in situations in which the magnitude of a signal must be maintained within boundaries for smooth system operation. For example, in a design in which the error signal driving the controller can reach very large values, it might be best to limit the error magnitude at the controller input to prevent excessive controller output magnitude.

Important Point

Be careful when placing a limiter on a signal that is an output (even indirectly) from an integrator. Integration takes place in proportional plus integral (PI) and proportional plus integral plus derivative (PID) controllers and could occur in a transfer function or state-space linear system. A linear system performs integration if it has one or more poles located at the origin of the complex plane. Placing a limiter on an integrator output leads to exactly the same problem discussed in Chapter 2: integrator windup. The actuator saturation described in that chapter has the same effect as placing a limiter on the controller output, which results in excessive overshoot, slow convergence to the commanded value, and potential oscillation and instability. If a limiter must be placed on a signal that has been integrated, try using the approach described in Chapter 2 for turning off the integration action when limiting is occurring. This reduces integrator windup while allowing the benefits of limiting controller signal magnitudes.