Key Causes of Uncertainty in Control Systems

One of the objectives of a control system is to achieve good plant performance in the face of uncertainty. The major sources of uncertainty in control are:

• Unmeasurable perturbations
• Modelling errors

Unmeasurable Perturbations

Unmeasurable perturbations produce output deviations. With a controller in place, the achieved deviations must be below a user-defined bound.

Modelling Errors

Modelling errors can be classified into three categories:

• Parameter uncertainty
• Unmodeled dynamics
• Non-linearity

Parameter Uncertainty

Parameter uncertainty originated by uncertainty in physical parameters. Parameter uncertainty may be accommodated with high-gain regulators in some instances.

Unmodeled Dynamics

Unmodelled dynamics i.e. neglected delays and fast time constants. The order of real plants is infinite (partial differential equations) and lumped parameter models are only approximations. In most cases, these approximations are intentionally made to keep the problem traceable. For example:

• Multi-loop control disregards the non-diagonal terms in tuning each loop. The cross-coupling is a modelling error that should be appropriately withstood.
• Low-order models are typically used to avoid modelling cost. For instance, modelling a distillation column with experimental first-order and delay models, instead of a detailed one based on thermodynamics, etc.

Non-linearity

Linear regulators must be at least robust to smooth non-linearities on the process. As a matter of fact, practical requirements usually require appropriate behaviour in the face of non-smooth non-linearities like hysteresis or backlash that occur mostly with valves and other mechanical actuators.

Take note of the fact that, modelling errors can change with time, due to plant aging or component replacement; significant modelling errors need to be considered in time ahead irrespective of the initial effort devoted to modelling.

Also read:

• The Performance Limits for PID Controllers
• 5 Control Techniques – Their Features & Applications
• What is Selective Control?
• How to Tune the PID Controller