Hi Avinash,

I think Dr. Rano has explained pretty well. To enhance your understanding on the topic, you can perform a simple experiment as explained below:

Given a 2nd-order system y''(t) + y(t) = u(t) with a set of initial conditions {y(0), y'(0)}, the following control law

u(t) = 2e−t (c2 t + c1 − c2)

where

c1 = y(0); and

c2 = y'(0) + c1

guarantees a critically-damped response that all eigenvalues with strictly negative real parts. The generalized control law remains valid for any arbitrarily set of initial conditions as long as u(t) is within the limits of the actuator. If a different set of c1 and c2 independent of initial conditions is arbitrarily chosen, but close to the values of c1(y(0)) and c2(y(0)), then the output response will be stably bounded. However, if they deviate far from c1(y(0)) and c2(y(0)), then you will get an unstable response.

Note that the proposed control law is not unique and it is derived from the knowledge of a desired critically-damped system response, y''(t) + 2y'(t) + y(t) = 0. From the result, you can easily formulate the initial conditions-dependent stability criterion, and find the answer to your own question.

Example: If {y(0), y'(0)} = {1, 1}, then u(t) = 2e−t (2t − 1) produces the following response.

Hi Avinash,

Generally I would agree with the response of Dr. Rano that by using open loop control the system can't be made globally asymptotically stable. Moreover, the open loop control is not robust as compared to closed loop system, therefore, it can not catter external disturbances, modeling inaccuracies and parametric variations