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When we are dealing with control we mostly have in mind feedback control since analysis and synthesis of feedforward control is straightforward.
Two degrees of freedom controllers
Control scheme contains two controllers Ra1 and Ra2 (Rb1 and Rb2 respectively). This control scheme is able to fulfill requirements on control performance and disturbance attenuation at the same time.
Types of controllers according to auxiliary power source requirement
self-acting controllers - They do not contain a power source. They take energy from the controlled system for their operation (temperature control, humidity control, control of liquid level, etc. They are usually nonlinear. Control action is often limited to a finite set of values (often only two values as on and off). Typical examples are relay controllers used in fridges, irons, automatic chargers, etc. Properties: low price, simplicity, sometimes surprising control performance.
controllers with auxiliary power source - the heart of those complex devices is an amplifier. Reachable control performance is much higher which is proportional to costs and complexity. Static parameters are often assumed to be linear at least around some working point. Control action is limited by physical limits.
Digital and analog control
Types of controller according to a way of operation
continuous time
discrete
quantized - discrete in magnitude
Basic controller contains one or multiple of following basic terms.
P – proportional
D - derivative
I – integration
We often deal with combination of previous terms: PI controller, PD controller, PID controller. In practice we can meet with other types like PI-D, I-PD, βPID
DESCRIPTION OF BASIC CONTROLLER PARTS
Proportional controller
Direct proportion exists between control action and control error x(t) = r0e(t). Transfer function is a constant:
Step response of P controller:
Proportional controller - F(γω)
Frequency response in complex plane - Nyquist plot Frequency response in logarithm coordinates - Bode plot
Integral controller
Description in time domain It corresponds to transfer function
It can be expressed using gain ri or using time constant Ti which is given as inverse of gain Ti = 1/ri. Integral term deteriorate dynamic properties of the controller. It slows down control action. In some cases it is the only possibility how to reach zero steady state error. It is helpful in disturbance attenuation.
Integral controller - cont.
Frequency response in complex plane - Nyquist plot Frequency response in logarithm coordinates - Bode plot
PD-Controller
Control action is composed from two parts:
one which is proportional to control error - constant r0
second which is proportional to derivative of control error - constant rd
The transfer function from the previous differential equation
Following relationship holds for contants above KR = r0; TD = rd /r0
PD Controller is not causal, rd is area of impulse in time zero of h(t). Derivative term improves dynamic performance of closed loop system. It improves control speed. Realization constant is set with regard to noise (amplifies noise).