What is the difference between lead and lag compensation

You typically use it to improve your transient as you mentionned. You can think of it as a PD controller cascaded with a low-pass filter. I actually never used a PID with a pure derivative in real-life.

I have always used a PI controller cascaded with a lead compensator, which is almost the same as a PID but as the advantage of limiting the high-frequency gain, thus improving stability at high frequencies. However, you won't have an infinite DC gain. Think of it as a PI controller with a soft reset. I have also seen the term "leaky integrator" used. It could be useful as an alternative to a PI to prevent integrator windup, or if you want a PI controller with a soft reset to slowly reset the integrator.

I have never really used one in real-life. Because, I use appropriate anti-windup strategies. And in the few cases where I needed a "soft reset" for my integrator for a PLL , I implemented a conditional soft-reset that was only enabled in certain conditions.

Sign up to join this community. Now substitute the value of I s in the above equation, we will have,. On simplifying,. On simplifying we will get,.

On cancelling like terms from numerator and denominator, we will get. In generalized form. So, on comparing,. Thus, in case of the lag lead compensator, a lead angle is added by the phase lead portion whereas attenuation near the crossover frequency is provided by the phase lag portion.

So, the magnitude will be:. Hence, the phase angle will be. So, we can say, a lag lead network provides a quick response with good accuracy. Thus, the result of a lag compensator is that the asymptotes' intersection is moved to the right in the complex plane, and the entire root locus is shifted to the right as well.

It was previously stated that a lag compensator is often designed to minimally change the transient response of system because it generally has a negative effect. If the phase-lag compensator is not supposed to change the transient response noticeably, what is it good for then? The answer is that a phase-lag compensator can improve the system's steady-state response.

It works in the following manner. At high frequencies, the lag compensator will have unity gain. In MATLAB, a phase-lag compensator C s in root locus form is implemented by employing the following code where it is again assumed that z and p are previously defined.

A first-order phase-lag compensator also can be designed using a frequency response approach. A lag compensator in frequency response form is given by the following. The phase-lag compensator looks similar to phase-lead compensator, except that a is now less than 1. The main difference is that the lag compensator adds negative phase to the system over the specified frequency range, while a lead compensator adds positive phase over the specified frequency.

A Bode plot of a phase-lag compensator has the following form. The main effect of the lag compensator is shown in the magnitude plot. The lag compensator adds gain at low frequencies; the magnitude of this gain is equal to a. Figure 4. Graphical illustration of root locus existence shaping and the concept of pole zero placement using a pseudo system S and a pseudo lag controller C.

Figure 5. Root locus of the system incorporated with the designed lag controller. Figure 6. Illustration of the design details of the phase-lag controller.

Figure 7. Graphical illustration of effects of a phase-lead controller on root locus using a pseudo system S and a pseudo lead controller C. Figure 8. Illustration of the design details of the phase-lead controller. Figure 9. Root locus of the system incorporated with the designed lead lag controller. Figure Illustration of the design details of the phase-lead lag controller. Illustration of the design details of the cascaded lead controller. Comparative analysis of closed-loop results using PI, lead, lag, and lead-lag controllers.

Comparative analysis of closed-loop results using cascaded lead controller and PI controller. Table 4. Controller performance characteristics a comparative analysis.

References I. Smith and P. View at: Google Scholar I. View at: Google Scholar E. Syaie, M. Rami, and F. Simalatsar, M. Guidi, and T. Marsh, M. White, N. Morton, and G. Schnider, C.

Minto, P. Gambus et al. View at: Google Scholar H. Schaller, J. Lippert, L. Schaupp, T. Pieber, A. Schuppert, and T.

Kaya, N. Tan, and D. Li, K. Ang, and G. Hodel and C. Mantz and H. Rohitha, S. Senadheera, and J. Zanasi and S. Wang and Y. View at: Google Scholar N. Messner, M. Bedillion, L. Xia, and D. Flores, A. Valle, and B. Zanasi, S. Cuoghi, and L. View at: Google Scholar K. Abdul Jaleel and N. View at: Google Scholar A. Dass and S. Sekara and M. Goswami, S.

Sanyal, and A. Sajnekar, S. Deshpande, and R. Tan, K. Teoh, and L. Myers, Y. Li, F. Kivlehan, E.