### Glossary of Control Engineering Terms - P

Padé Approximation: A transfer function that approximates dead-time. A first order approximation of a dead-time of Td seconds is (1 - 0.5Tds)/(1 + 0.5Tds). More accurate higher-order approximations are available.

Phase Angle: See phase shift.

Phase Margin: The difference in phase at the frequency where the combined process and controller amplitude ratio is 0 is the PHASE MARGIN.

Phase Shift: This is the angle (in degrees) between a sine wave input into a system and the resulting sine wave output (for a linear system). This usually varies with frequency, with slower frequencies usually having a small phase shift and higher frequencies having more phase shift. If the output is in anti-phase with the input (i.e. at a minimum when the input is at a maximum, and vice versa) then that has 180 degrees of phase shift. For an integrator (or integrating processes) the phase shift is -90 degrees at all frequencies (look at the integral of a sine function if you're not convinced).

PID Controller: Controllers are designed to eliminate the need for continuous operator attention. Cruise control in a car and a house thermostat are common examples of how controllers are used to automatically adjust some variable to hold the process variable (or process variable) at the set-point. The set-point is where you would like the process variable to be. Error is defined as the difference between set-point and process variable.(error) = (set-point) - (process variable). The output of PID controllers will change in response to a change in process variable or set-point.

Plant: Another name for the system or process being controlled.

Plant Output: What you are trying to control. Also called Process Variable.

PLC: Programmable Logic Controller. These computers replace relay logic and usually have PID controllers built into them. PLCs are very fast at processing discrete signals (like a switch condition). The most popular PLC manufacturers are Allen Bradley, Modicon, GE, and Siemens (or TI). PLC (Programmable Logic Controller) A class of industrially hardened devices that provides hardware interface for input sensors and output actuators. PLCs can be programmed using relay ladder logic to control the outputs based on input conditions and / or algorithms contained in the memory of the PLC.

Predictive Control: A form of control that predicts what the process status will be at some point in the future and, using this information, modifies control outputs to get the process state to the desired value. Feed-forward is a very basic form of predictive control.

PV or Process Variable: What you are trying to control: temperature, pressure, flow, composition, pH, etc. Also called the measurement.

Pole: A root of the transfer function denominator polynomial. Can be real or complex conjugate. Poles with a negative real part are stable. The poles determine the transient response of the system. Fast poles are much further away from the stability boundary than other poles and the transients associated with these poles will decay faster. Dominant poles are closer to the stability boundary and being slow will dominate the transient response.

Pole Placement: Moving the open-loop poles of a system to specified closed-loop pole positions which will give a desired closed-loop dynamic response.

Process: Another name for the system or plant being controlled.

Process Uncontrollability (Pu): Pu = dead-time/time constant. A measure of how well a process or system can be controlled with a simple PID controller. If Pu < 1 then good control is possible, if Pu > 1 then the controller may need to be detuned to maintain stability. If Pu >> 1 then a Smith Predictor or Predictive Control may be required.

Process Variable: Another name for the plant or system output, the thing that you are trying to control.

Proportional Gain: This is the "P" part of the PID controller.

PWM (Pulse Width Modulation): A switch-mode control method used in amplifiers and drivers to control motor voltage and current to obtain higher efficiency than linear control. PWM refers to variable on/off times (or width) of the voltage pulses applied to the transistors.