WARNING: YOU NEED TO HAVE A BACKGROUND KNOWLEDGE ABOUT CONTROL OR TRANSFER FUNCTION IN ORDER TO UNDERSTAND THIS ENTRY.
I like the thought that my Control lecturer gave us, last 2 weeks about life. I never think that way, and never relates my life with other things - Control.
The argument is like this:
In life, generally speaking, we never tired of wanting more.It is because of our achievement in the past, we are happy with the achievement that we used to get and that's why, we want more and more of them. And whether we realized or not, the more we get, the more we want. We never stop wanting them. But, the more we want, the more burden we get.
I give a simple example: MONEY. We never stop wanting money. But, the more we get, the more we want,isn't it? So, to get more money, we have to work more, which means we add our burden more by working really hard. Why we want more? because we get joy and happiness if we get more. Naturally, human wants to live with joy and happiness for the whole life and this cycle will never stop.
Let x be the level of achievement and t is the time;
Let the plot of x vs t shows a step changes (when t=0, x is a real number, otherwise is zero);
Let y1 be the level of joy, and t is the time;
Let the plot of y1 vs t shows an exponential graph with negative time constant (means as t->infinity, y1->0);
Let y2 be the level of burden, and t is the time;
Let the plot of y2 vs t shows an exponential graph as well with negative time constant, but it reaches a steady state after some time (steady state is a real number-not equal to 0);
If we plot the graphs, we can clearly see that the level of joy(y1) is the derivatives of the level of burden(y2), which is make sense, because intuitively, the level of joy will fade out with time if we don't keep increasing the rate of convergence of the burden graph.
If we take the transfer function for y1 on x;
Y1(s)/X(s) = K1 s/(1 + t1s)
And if we take the transfer function for y2 on x;
Y2(s)/X(s) = K2/(1 + t2s)
where K1,K2 are both the gain.
What do we want? We want to get more joy than burden;
Y1 > Y2;
Therefore Y1(t) - Y2(t) > 0; for all t;
Y1(s) - Y(s) > 0
K1 s/(1 + t1s) - K2 s/(1 + t2s) = 0
K1s(1+t2s) - K2(1+t2s) = 0
(K1t2 - K2t1)s^2 + (K1-K2t1)s - K2 = 0
Let the roots of the polynomial be s1, s2:
x(t) = A1 exp(s1t) + A2 exp(s2t);
Therefore, to get a higher level of achievement (x(t)), we should have a higher value of the exponential, which means, a higher value of s1 and s2, or at least one of the roots must be a real number.
For a conclusion, we can clearly see, we couldn't get rid of getting burden more if we want to have more joy as well as the achievement.
p/s:ita dah bosan dgn stochastic.