HRRE materiály ke zkoušce

Step response (transient response) Frequency response in complex plane - Nyquist plot

Frequency response in logarithm coordinates. Bode plot.

PI-Controller

Similarly as in case of PD controller, two terms are used in PI controller. As it comes from its abbreviation these are proportional one and integral one.

Description in time domain:

Graphs:

PID-Controller

This is the most complex controller from the category of basic controllers. Its output is composed from all three basic terms we were talking about up to now: (Figures)

Very important form is the one with constants KR gain, TD derivative time constant, TI integral time constant (parallel connection of P, I a D controllers). Enables to incorporate limitation of control action and anti wind-up.

The last form is not completely equivalent with previous two since it does not enable to assume complex conjugate zeros of the controller which is usually not important for practical usage.

Condition of causality is fulfilled with adding first order low pass filter with time constant ε - guarantees that derivative term is feasible. This time constant is usually set with regard to level of noises.

PERFORMANCE INDEX FACTORS FOR EVALUATION OF DYNAMIC CONTROL PERFORMANCE

Integral criteria are able to serve as a criteria (cost function) for evaluation of dynamic control performance. They come from course of control error in time domain. Following criteria were defined

• Integral Error (IE)

• Integral Absolute Error (IAE)

• Integral Squared Error (ISE)

• Integral Time-weighted Absolute Error (ITAE)

  • less oscillating optimal result comparing with quadratic criteria

  • weighted criteria - weight is increasing linearly with time

  • analytical solution is not possible, result comes usually from simulation

Pozn. Dále číst ve skriptech na straně 93 (94)

Practical criteria

The most widely used measure of practical control performance is the decay ratio as it gives good indication of the quality of the controlled response. An often used rule for controller tuning is ’one-quarter decay ratio’, where the controller is tuned to produce a decay ratio of ¼ (the second peak is a quarter the height of the first).

• Percentage overshoot

• Number of visible overshoots - Decay ratio.

CONTROLLER DESIGN METHODS

Control circuit design usually starts with the discussion between control engineer and technologist from given industrial branch. Together they define controlled variables, control actions and they also study possible disturbances. Properties of controlled system are analyzed and requirements on control performance are stated.

Control circuit synthesis steps:

• selection of sensors, actuators, power amplifiers and controllers,

• selection of control structure,

• tuning of controller parameters.

Everything is derived from requirements on control performance and from properties of controlled system.

Following scenarios can be solved:

• we can choose structure and also its parameters,

• control structure is given and its parameters are tunable,

• control structure and some of its parameters are given and the rest of the parameters is tunable.