The Performance Limits for PID Controllers

PID Controllers can be applied successfully to most control problems in process control, electrical drive systems and servo mechanisms due to the fact that most of these processes have a dynamic behaviour that can be adequately approximated by a second-order process. However, the PID controller is not enough to control processes with additional complexities like time delays, significant oscillatory behaviour (complex poles with small damping), parameter variations and multiple-input-multiple-output systems.

Let us look at some of these complexities and how they influence the performance PID Controllers:  

Time Delays

In process industries, time delays usually occurs because of the presence of distance logs, recycle loops or the dead time associated with composition analysis. The time delay makes information from the true process variable change arrive later than the desired time to the controller. This limits the performance of the control system and may lead to system instability.

Any system with time delay that is controlled by a PID controller behaves quite sluggishly. This is due to the fact that the gain has to be quite small so that instability is not risked.

Related: Proportional-Integral-Derivative (PID) Control Systems

Complex Dynamics

Due to the limited number of parameters, the PID controller cannot arbitrarily influence a process with high order dynamics. In schemes with significant oscillations a higher order regulator is required. For example, the PIPI controller in electrical drive systems, where the order has been extended by a low pass filter (note, PIPI controller consists of two PI controllers in series or a PI controller in series with a low pass filter). The purpose of the extra low pass filter is to limit the high frequency signals. In mechanical drive systems there may be resonance oscillations that are appropriately dampened by such a filter.

Consider cases where the systems have many inputs and outputs, where there are significant couplings between the systems. The control task cannot be solved by a simple controller based on one input and one output. Instead one control signal has to be based on several measurements signals. One way to synthesize this type of controller is by state variable feedback.

Related: Digital PID Controllers

Parameter Variations

There are many processes where the process parameters change with operating conditions. If the variation of the process gain is known at different operating points it can be stored in a table. The controller can be tuned according to such a table and its tuning calculated in advance. This gain-scheduling is a common procedure in many applications, for instance, in steam boiler control (different control setting at different power levels) or in aircraft control (different altitude controller settings for different altitudes).

In a number of systems, process dynamics is unknown with constant parameters and in other systems the parameters change slowly with time. This is may be due to a number of reasons for the gradual changes. The piping in a process may be gradually clogged by material and this may change flow rates or heat transfer properties. In systems such as the air-fuel ratio control in a combustion engine, the sensor changes its gain and bias in an unknown way over time. In a biological fermenter or wastewater treatment plant, new organisms may appear and change the pattern of the oxygen uptake rate. Normally, systems with a low order dynamics are simple to control once the parameters are known and constant. A PID controller is enough in most cases.  However, if the parameters are slowly changing the tuning will be quite poor most of the time. One solution to this issue is automatic tuning of the PID controller i.e. auto-tuner. The tuning is initiated by the operator. The auto-tuner then excites some small disturbances to the process to find out its dynamics and computes the PID controller parameters from the process response. The parameters are kept constant until the operator initiates a new tuning.

Also read: How to Tune the PID Controller