Pid Tuning Method

PID TUNING METHOD

Tuning • Tuning a control loop is arranging the control parameters to their optimum values in order to obtain desired control response. At this point, stability is the main necessity, but beyond that, different systems leads to different behaviours and requirements and these might not be compatible with each other.

Tuning • In principle, P-I-D tuning seems completely easy, consisting of only 3 parameters, however, in practice; it is a difficult problem because the complex criteria at the P-I-D limit should be satisfied. P-I-D tuning is mostly a heuristic concept but existence of many objectives to be met such as short transient, high stability makes this process harder.

Tuning • For a system to operate properly, the output should be stable, and the process should not oscillate in any condition of set point or disturbance. However, for some cases bounded oscillation condition as a marginal stability can be accepted. • In order to achieve optimum solutions Kp, Ki and Kd gains are arranged according to the system characteristics.

TUNING METHOD • Manual Tuning Method • Ziegler-Nichols Tuning Method • Cohen-Coon Tuning Method

Manual Tuning Method • Manual tuning is achieved by arranging the parameters according to the system response. Until the desired system response is obtained 𝐾𝑖 , 𝐾p and 𝐾𝑑 are changed by observing system behaviour. • Although manual tuning method seems simple it requires a lot of time and experience

Ziegler-Nichols Method • Ziegler-Nichols proposed rules for determining values of the proportional gain 𝐾𝑝, integral time 𝑇𝑖, and derivative time 𝑇𝑑, base on transient response characteristics of a given plant. • Such determination of the parameters of PID controllers or tuning of PID controllers can be made by engineers on-site using experiments on the plant. • There are two methods called Ziegler–Nichols tuning rules: • First method (open loop Method) • Second method (closed Loop Method)

Ziegler-Nichols FIRST Method • In the first method, we obtained experimentally the response of a plant to a unit step input,

• If the plant involves neither integrator(s) nor dominant complexconjugate poles, then such a unit-step response curve may look S-shaped.

Zeigler-Nichols First Method • Where : L=Delay time T=Time constant • This method applies if the response to a step input exhibits an S-shaped curve.

• Such step-response curves may be generated experimentally or from a dynamic simulation of the plant.

Zeigler-Nichol’s Tuning rule based on step response of the plant

Zeigler-Nichols First Method

Zeigler-Nichols Second Method • In the second method, we first set 𝑇𝑖 = ∞ and 𝑇𝑑 = 0. • Using the proportional control action only (as shown in figure), increase Kp from 0 to a critical value Kcr at which the output first exhibits sustained oscillations.

Zeigler-Nichols Second Method • If the output does not exhibit sustained oscillations for whatever value Kp may take, then this method does not apply.

Zeigler-Nichols Second Method

Zeigler-Nichols Second Method

EXAMPLE