5. Feedback control systems

Feedback control is an action by which PID controllers as well as the controllers based on advanced control strategies implement their control action. In feedback control system, the controlled variable is measured and compared to the setpoint. Subsequently, an error signal is generated by subtracting the setpoint from the value of the controlled variable. Then the controller calculates the the appropriate corrective action, to be implemented by the manipulated variable, by using the value of the error signal.¹⁶

5.1 PID controller

In feedback control applications, the most widely used form for the control algorithm is PID controller equation given below

p(t) = p + K_c [ e(t) + (int (e(t)dt))/T₁ + T_Dde(t)/dt ]                                        (24)

where, p(t) = controller output
p = bias, which is set at the desired output when the error signal is zero
e(t) = controlled variable’s error
int (e(t)dt) = integral of e(t)
K_c = controller gain
T₁,T_D = controller parameters

5.2 Stability considerations

It should be borne in mind that the feedback control can cause oscillations in closed - loop systems. Depending on the situation, these oscillations may or may not damp out quickly. In case where the oscillations may persist, the closed loop system is said to be unstable. This undesirable behavior can usually be eliminated by proper adjustments of the PID controller constants.⁴

5.3 Further feedback control techniques

While the single-loop PID controller is satisfactory in many process applications, its performance is not satisfactory in many processes, e.g., the ones with slow dynamics, frequent disturbances, or multivariable interactions. In that case, various strategies like  cascade control, time - delay compensation, and feedforward control can be employed to improve the performance. Excellent review about these techniques has been given by Fordyce et al.⁴

5.4 Feedback control of multivariable systems

Many processes contain a number of manipulated variables and controlled variables. Such a process is called multivariable system. A multivariable control system can be treated as a control system comprising of several single - loop controllers. The techniques discussed earlier can only be used if the interactions between these controllers are not strong. If such is not the scenario, the controllers need to be detuned to reduce oscillations.⁴ A better approach is to utilize multivariable control techniques such as optimal control which is discussed in next section of this paper.