Doplněk k materiálům ke zkoušce

are simple, efficient and effective in wide array of applications – in fact the majority of today’s controllers are PID

• In the proportional path the error term is multiplied by a constant KP

• In the integral part the error is multiplied by KI and then integrated

• and in the derivative path it is multiplied by KD and then differentiated

• those three parts are summed together to produce the controller output

K ……… gains (can be adjusted or tuned to a particular plant with defined set of requirements; by changing these values we are adjusting how sensitive the system is to each of these different paths (P, I or D path) + you can remove each of those paths by setting its gain to zero)

Advantages and disadvantages of I term

- 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.

Advantages and disadvantages of D term

-

+ Derivative term improves dynamic performance of closed loop system.
It improves control speed.
Realization constant is set with regard to noise (amplifies noise).

PERFORMANCE INDEX FACTORS FOR EVALUATION OF DYNAMIC CONTROL PERFORMANCE

Integral (used) criteria

Integral error (IE) (Lineární kritérium)

Substraction of steady state error e(∞) ensures convergence of the integral to finite value.

Integral Absolute Error (IAE) (Usměrněné lineální kritérium)

Integral Squared Error (ISE) (Kvadratické kritérium)

■ higher control errors are assumed with higher weight

■ optimal solution is highly oscillating

Integral Time-weighted Absolute Error (ITAE) (ITAE kritérim)

• ■ 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

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.

Ziegler–Nichols method

The Ziegler–Nichols method is a classic experimental method of tuning a PID controller.

It is performed by setting the I (integral) and D (derivative) gains to zero. The "P" (proportional) gain, is then increased (from zero) until it reaches the ultimate gain , at which the output of the control loop has stable and consistent oscillations. and the oscillation period are used to set the P, I, and D gains depending on the type of controller used.

1) shut off I and D control -> P controller
2) put the controller in automatic -> this will create a closed loop
3) alter the controller gain until the response that is seen is undamped (the oscillations are neither growing or falling) – then we can see consistent oscillations