Imagine taking a shower from a two-knob faucet. You want to set the rate of water flow and its temperature so that the shower is effective and comfortable. You can control the hot water flow and the cold water flow separately. Throughout your shower, there may be "disturbances" in the form of changes in water supply temperature and pressure.
So how do you regulate your shower?
This is the structure of a basic feedback control loop. Information from the process (water flow and temperature) is "fed back" by a measurement device (you) through a controller (you again) to a control element (the knobs) to change the process input.
All control systems have these same basic components:
The system can be represented by a block diagram where lines are used to represent variables or signals and boxes for actions.
Block diagrams represent the logic and mathematical model of a control loop. We might also choose to represent the equipment used to construct the loop in a piping and instrument diagram or P&ID. Complete P&IDs show every piece of equipment, wiring, etc., that need to be installed, and so can be very complex. For our purposes, we just want to see the main pieces, so a simplified drawing is used.
Table 1.1 of your textbook has a handy list of commonly used symbols for these diagrams.
When an engineer sets out to design a control system, the steps are:
In this class, we will deal mainly with the tools and concepts needed to model the process, examine the stability, and select and tune controllers.
Steady State: A steady state system does not change with time. Mathematically, this means the time derivatives in the balance equations (the accumulation terms) are zero. Often, systems will reach steady state if given a long time to settle -- usually, real systems don't get the time. This leads to another mathematical approximation -- steady state is the behavior of the system as time approaches infinity. Some people use the words static or stationary as synonyms for steady state.
Dynamic (or transient) systems are time dependent. All real systems are dynamic; this makes process control necessary. Dynamic systems must be modeled using differential equations, unlike steady state systems where algebraic systems will suffice.
Inputs and Outputs are not necessarily material flows. An input is a variable that causes an output to change. Both inputs and outputs may be measurable or they may not. Disturbances are inputs that cannot be adjusted, and often they are not measurable.
Error is the difference between the measured behavior of a process output and its desired behavior or setpoint. Never forget that the measured values of the outputs are only representations of the real values, and may be limited in accuracy.
Feedback Control: information from an output of a system is used to adjust a manipulator to change an input to the system to try and compensate for disturbances after they have changed the system.
Feedforward Control: information from measured disturbances is used to adjust a manipulator to try and compensate for disturbances as they occur. Feedforward allows for the possibility of "perfect control", but only if all disturbances are measured and the adjustments are fully understood. This means you must have a complete and very accurate model of the process -- not an easy achievement. Feedback control adjusts for all disturbances and does not require an exact process model.
Negative feedback reduces the difference between the actual and desired values, so it is beneficial. Positive feedback increases the difference, so it is undesired.
When a system is operating without control, we say it is operating Open Loop. A Closed Loop system has controllers on-line.
One of the most important things we will be watching is the stability of the system. The error of an unstable system becomes larger and larger (unbounded) with time, often leading to undesirable consequences.
References:
R.M. Price
Original versions: 9/29/93, 1/10/94; 10/15/93
Modified: 1/6/95, 12/15/95, 12/7/96; 3/1/96, 3/23/98; 4/24/2003,
8/10/2004
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