# 二阶系统 PD 校正后在阶跃响应下时域指标的计算

## 一般形式的计算

### 基础公式

$$G (s) = \frac {C (s)}{E (s)} = \frac {K\left (T_{d} s+1\right)}{s\left [s /\left (2 \zeta \omega_{n}\right)+1\right]} \tag {1.1}$$

$$\Phi (s)=\frac {\omega_{n}^{2}}{z} \cdot \frac {s+z}{s^{2}+2 \zeta_{d} \omega_{n} s+\omega_{n}^{2}} \tag {1.2}$$

$$\zeta_{d}=\zeta+\frac {\omega_{n}}{2z} \tag {1.2.1}$$

$$C (s)=\frac {\omega_{n}^{2}}{s\left (s^{2}+2 \zeta_{d} \omega_{n} s+\omega_{n}^{2}\right)}+\frac {1}{z} \frac {s \omega_{n}^{2}}{s\left (s^{2}+2 \zeta_{d} \omega_{n} s+\omega_{n}^{2}\right)} \tag {1.3}$$

$$c (t)=1+r \mathrm {e}^{-\zeta_{d} \omega_{n} t} \sin \left (\omega_{n} \sqrt {1-\zeta_{d}^{2}} t+\psi\right) \tag {1.4}$$

$$r=\sqrt {z^{2}-2 \zeta_{d} \omega_{n} z+\omega_{n}^{2}} /\left (z \sqrt {1-\zeta_{d}^{2}}\right) \tag {1.5}$$

$$\psi=-\pi+\arctan \left [\omega_{n} \sqrt {1-\zeta_{d}^{2}} /\left (z-\zeta_{d} \omega_{n}\right)\right]+\arctan \left (\sqrt {1-\zeta_{d}^{2}} / \zeta_{d}\right) \tag {1.6}$$

# To：Cheems of the future…

To: cheems of the future…

Hello, long time no see.

I am the past you.

When you think of this letter…

Have you fulfiled our dream?

Or, not done by life?

I don’t know.

But, cheems…

Never stop chasing.

I know it may be difficult…

Even if I tried hard, the flame of hope can’t be lit.

But, cheems…

If one day…

I give up.

Bury our dreams..

Well, no matter how many times.

Pick up your shovel again and dig out the dream again!

Our stories should not be buried deep in the ground…

But should store in the sky!

No matter how many times we’ve been knocked down,

don’t forget the power of dreams.

Go to the end of the Earth.

But it’s not just the end of the Earth…

To see the endless wilderness,

go and see the mountains stretching thousands of miles,

go and see the waterfall flowing straight down,

go and see the clear and clean lake,

no why, just because I wanted to go.

Isn’t that the best life?

# You're Not Late! You're Not Early

New York is 3 hours ahead of California,

but it does not make California slow.

Someone graduated at the age of 22,

but waited 5 years before securing a good job!

Someone became a CEO at 25,and died at 50.

While another became a CEO at 50,and lived to 90 years.

Someone is still single,while someone else got married.

Obama retires at 55,but Trump starts at 70.

Absolutely everyone in this world works based on their Time Zone.

People around you might seem to go ahead of you,

some might seem to be behind you.

But everyone is running their own RACE, in their own TIME.

Don’t envy them or mock them.

They are in their TIME ZONE, and you are in yours!

Life is about waiting for the right moment to act.

So, RELAX.

You’re not LATE. You’re not EARLY.

You are very much ON TIME, and in your, TIME ZONE Destiny set up for you.