这样理解吗

是这样理解吗？

没太听太清

我没听太清楚。

so let's have a look at the movie koya river together so this image shows the working principle. of moving coil meter. there is a magnet inside. of the moving coil meter. and there is also a circuit. so once the circuit has current, because of the magnet, the circuit will rotate. that's the reason. that's the reason you can see the pointer. The pointer is moving, right? so it's exactly the working principle of moving coil meter.

那么，我们一起来看一下《科亚河》这部电影。这张图片展示了它的工作原理。也就是动圈式仪表的工作原理。里面有一个磁铁。就是动圈式仪表里的磁铁。还有一个电路。所以，一旦电路中有电流通过，由于磁铁的作用，电路就会发生旋转。这就是原因。这就是为什么你能看到指针。指针在移动，对吧？所以，这正是动圈式仪表的工作原理。

and we know if you want to measure current, we have to connect moving coil meter in series with the circuit. if you want to measure voltage, we have to connect the moving coil meter in parallel.

我们知道，如果你想测量电流，就必须将动圈式仪表串联进去。与电路串联。如果你想测量电压，就必须将动圈式仪表并联在电路中。

in parallel with the circuit.

也就是与电路并联。

but sometimes the current is quite large. so in order to measure, a very large current, you have to use a shunt resistor. to expand the range. You have to use a shunt resistor to expand the measuring range.

但是，有时候电流会非常大。所以，为了进行测量，对于非常大的电流，你必须使用分流电阻。这样可以扩大测量范围。你必须使用分流电阻来扩展测量范围。

and in ammeter, the shunt resistor is connected in parallel. in parallel with the internal resistance.

在电流表中，分流电阻是并联连接的。与电流表的内阻并联。

in a voltmeter, the multiplier resistor is connected in series with the internal resistance. in order to expand the measuring range.

而在电压表中，倍率电阻是与内阻串联的。这也是为了扩展测量范围。

Because the first scale deflection is actually quite small.

因为第一次满偏的偏转其实非常小。

for example, it's outside of the range. outside range of 50 micro, and so we have to expand. But how can we achieve this? We just use a shunt resistor. so that we can get

比如说，它超出了量程。超过了50微安的量程，所以我们必须对其进行扩展。但是，我们该如何实现这一点呢？我们只需要使用一个分流电阻。这样我们就能获得

a very large current.

非常大的电流。

And for the voltmeter is different. It's a multiplier resistor to expand the measuring range. So that we can measure large voltage.

而对于电压表来说，情况则不同。它是通过倍率电阻来扩展测量范围的。这样我们就能测量高电压了。

Yes, so that's all the content. and our last page.

是的，以上就是全部内容。这是我们的最后一页。

And here there are some photos. about the here the first one, the first photo is voltmeter. And the second photo is the ammeter. And we use these devices to measure voltage or current.

这里有一些照片。首先，第一张照片是电压表。而且，第二张照片是电流表。我们使用这些设备来测量电压或电流。

And this is the component inside. inside of the moving coil ammeter.

这是内部的组件。它是动圈式电流表的内部结构。

Just like we have mentioned in the slides, there is a magnetic field. This is the cylinder. The cylinder is the magnetic field. And there is a moving coil.

正如我们在幻灯片中提到的，这里有一个磁场。这是一个圆柱体。这个圆柱体就是磁场。里面还有一个动圈。

inside, moving coil inside. and once there is a current, flowing. flowing in the moving coil, the pointer will be rotated. so then you can see how large or how large the voltage is.

在内部，有一个动圈。一旦有电流通过，就会产生电流。在动圈中流动，指针就会发生偏转。这样，你就能看出电流的大小了。或者电压的大小。

然后我当时看到那个要一直发消息在那 在那 it gives you the value. or the value of the voltage.

然后我当时看到那个一直在发消息，就在那里。它会显示数值。或者是电压的数值。

yeah, you probably have also have a driver license. and you have ever been driving a car. and there's also this kind of display in the car. and they also use this kind of pointer.

是的，你可能也有驾照。你肯定开过车。车里也有这种显示屏。他们也使用这种指针。

to show how high the speed is. or how high the rotation speed are. of the engine.

用来显示速度有多快。或者旋转速度有多快。也就是发动机的转速。

actually such kind of device is widely used.

实际上，这种设备被广泛使用。

there are many applications.

它有很多应用场景。

where the moving coil ammeter is applied. in our real world.

就是动圈式电流表的应用领域。在我们的现实生活中。

so this word just show some things photos. yeah, these two photos.

所以这一页只是展示了一些照片。对，就是这两张照片。

great. so apart from the moving coil ammeter, we also introduced the control system. so what is the control system? and how can we interpret it?

很好。那么，除了动圈式电流表之外，我们还介绍了控制系统。那么，什么是控制系统呢？我们该如何理解它？

right? so this is the task heading.

对吧？这就是任务标题。

and each block has its own modifying effect. on the input signal.

每个模块都有其独特的修改效果。作用于输入信号。

For the first block, it's an electrical signal.

以第一个模块为例，它是一个电信号。

so the first block has its own modifying effect.

所以，第一个模块具有其自身的修改效果。

the input working is a signal conditioner.

它的作用是一个信号调理器。

so we have introduced the different blocks. in your control system. and each block has a modifying effect, right?

所以，我们已经介绍了不同的模块。在你的控制系统中。每个模块都有修改作用，对吧？

and the modifying effect of each block can be defined as a gain. so each block has a gain. and they are represented by a symbol k.

而每个模块的修改效果，可以定义为增益。所以，每个模块都有一个增益。它们用符号来表示。就是字母K。

so in this block, each block has a gain.

所以，在这个框图中，每个模块都有一个增益。

can be multiplied together. to compute the system sensitivity.

它们可以相乘。用来计算系统的灵敏度。

when you multiply the gains together, you will get the system sensitivity.

当你把所有的增益相乘时，就会得到系统的灵敏度。

and here is an important definition. what is transfer function? transfer function is defined as the ratio between the output and input.

这里有一个重要的定义。什么是传递函数？传递函数的定义是，输出与输入的比值。

theta zero, theta o, theta o is the output. theta i is the input. so theta o divided by theta i is the transfer function. it can be exactly expressed by the product. of the gains.

Theta零，Theta o，Theta o就是输出。Theta i就是输入。所以，Theta o除以Theta i，就是传递函数。它可以精确地用乘积来表示。也就是增益的乘积。

but sometimes the control system is open loop. which means the output cannot affect

但是，有时候控制系统是开环的。这意味着，输出无法影响

the input. So this exactly here you can see, the key point is that the output is not used. it's not used to modify the input. So this is the definition, this is the property. property of open loop system. the output is not used to modify the input. so the output will not affect the input.

输入。所以，大家可以看到，这里的关键点是，输出没有被利用。它不会用来修改输入。所以，这就是定义，也是它的特性。开环系统的特性。输出不会用来修改输入。所以，输出不会影响输入。

so there is no feedback.

所以，没有反馈。

open loop system controlling the speed of a direct current motor.

开环系统用于控制直流电机的速度。

okay, if you have an open loop system, and suddenly you increase

好的，如果你有一个开环系统，然后突然增加

you want to maintain a system. so compare to the open loop, you can see there's the there's a block. which is exactly used for for feedback.

想要保持系统稳定。与开环系统相比，你可以看到，这里有一个模块。它正是用来实现反馈的。

if the output changes from the desired value.

如果输出偏离了设定值。

So in your DC motor example, if you just increase the load, increase the load of the output.

那么在你刚才的直流电机例子中，如果负载突然增加，输出的负载就会增加。

in a closed loop, you can increasing the current in the input.

但在闭环系统中，你可以增加输入电流。

speed will not be decreased.

这样速度就不会下降。

Because you know, you know how to put a speed, then you use this feedback. to change the inputs. For example, by providing large current.

因为你知道，你需要知道输出的速度，所以你就使用了这个反馈。通过改变输入来调整。比如，提供更大的电流。

so that the output speed will not be changed.

这样输出的速度就不会改变。

because now you have a feedback system. so you can change the inputs.

因为现在你有了一个反馈系统。所以你可以调整输入。

And actually, it includes four main components. The first one, you have the input signal, right? The input signal also defined as reference signal.

实际上，它包含四个主要组成部分。首先，是输入信号，对吧？输入信号也被称为参考信号。

because the feedback component, the feedback will be used to compare the output.

因为反馈组件会将输出与参考信号进行比较。

of the outcome achieved.

也就是实际达到的结果。

So this circle is exactly the

所以，这个圆圈正是

comparison. You have a very small error. So we don't have to change the output a lot. But if you have a big error,

比较器。这里的误差非常小。所以我们不需要对输出进行大幅调整。但如果误差很大，

we should change. Here you can see the four components. We have the input signal. setpoint i. And we have output signal. theta o. theta o is the output signal. And we have the comparator, right? comparator here is this circle. And we have a control system. these two blocks are the control system.

我们就需要进行调整。这里可以看到四个组成部分。首先是输入信号。也就是设定值I。还有输出信号。也就是O。O是输出信号。然后我们还有比较器，对吧？这里的比较器就是这个圆圈。此外，我们还有一个控制系统。这两个模块就是控制系统。

And each block has a gain.

每个模块都有一个增益。

And the feedback system also has a gain.

反馈系统也有一个增益。

and we use the gains in the feedback components.

我们在反馈组件中使用了这些增益。

but in this case, how the mission is defined as the ratio between the output and input.

但是在这种情况下，传递函数被定义为输出与输入的比值。

so how can we determine theta o?

那么，我们如何确定θo呢？

and we know here is the gain, right? this control system has the gain. g. so theta zero, theta o, theta o.

我们知道这里有一个增益，对吧？这个控制系统有一个增益。就是g。所以，θ0，θo，θo。

theta o equals to g. g is the gain. times the error.

θo等于g。g就是增益。乘以误差。

so theta o equals to g times the error. so theta i minus h times theta o. is the error. so the error we can get.

所以，θo等于g乘以误差。也就是θi减去h乘以θo。这就是误差。这样我们就能得到误差了。

need fix.

需要修正。

so theta zero, right, theta o, theta o equals to the gain times the error. so this is the first equation. and the error is the difference between the input

所以θ0，也就是θo，等于增益乘以误差。这就是第一个方程。而误差就是输入

and the output signal from the PID.

和PID输出信号之间的差值。

so we know e can also be expressed by theta o divided by g.

所以我们知道，e也可以表示为θo除以g。

and i minus theta o.

也就是i减去θo。

so we just repeat.

所以我们只是重复一下。

theta o is theta i minus h theta.

θo等于θi，减去hθ。

times g.

再乘以g。

so theta o divided by theta i

所以，θo除以θi

is the and sometimes even input.

就是输入。

and few minutes. Please, keep an eye on your control system. The value is quicker.

只需要几分钟。请大家注意观察你们的控制系统，数值变化得很快。

so this is the steady value. This is the steady value. This is the steady value. Quicker than our highly damped.

这就是稳态值。这就是稳态值。这比我们的强阻尼系统要快。

and for the control system, even if the output current varies, it's still

而对于控制系统来说，即使输出电流发生变化，它依然

stable.

保持稳定。

that's the basic introduction.

这就是基本的介绍。

Can you go through what we learned in our last lecture? The content was quite simple. We learned one concept, one definition: what a Bobby Koya meter is.

请大家回顾一下我们上节课学的内容。上节课的内容其实很简单，我们只学了一个概念、一个定义：什么是Bobby Koya表。

Let's look at the moving coil meter. This image shows the working principle of the moving coil meter. There is a magnet inside the moving coil meter, and there is also a circuit. Once the circuit has current, because of the magnet, the circuit will rotate. That is the reason you can see the pointer moving. This is exactly the working principle of the moving coil meter.

我们来看动圈式电表。这张图展示了动圈式电表的工作原理。动圈式电表内部有一块磁铁，同时还有一个电路。一旦电路中有电流通过，由于磁铁的作用，电路就会旋转。这就是你能看到指针转动的原因。这正是动圈式电表的工作原理。

As we know, if you want to measure current, we have to connect an ammeter in series with the circuit. If you want to measure voltage, we have to connect a voltmeter in parallel with the circuit.

正如我们所知，如果要测量电流，我们必须将安培表与电路串联。如果要测量电压，我们必须将伏特表与电路并联。

Sometimes the current is quite large. In order to measure a very large current, you have to use a shunt resistor to expand the measuring range. That is in an ammeter.

有时电流相当大。为了测量非常大的电流，你必须使用分流电阻来扩展量程。这是在电流表中。

In an ammeter, the shunt resistor is connected in parallel with the internal resistance. In comparison, in a voltmeter, the multiplier resistor is connected in series with the internal resistance in order to expand the measuring range.

在电流表中，分流电阻与内阻并联连接。相比之下，在电压表中，倍率电阻与内阻串联连接，以扩展测量范围。

FSD, full-scale deflection, is actually quite small. For example, it is only 50 microamperes—that is too small. But if we want to measure, for example, 5 amperes, that is outside the range of 50 microamperes. So we have to expand the measuring range. How do we achieve this? We just use a shunt resistor, so that we can measure.

满偏转（FSD）实际上非常小。例如，它只有50微安——这太小了。但如果我们要测量，比如说5安培，这就超出了50微安的量程。因此我们必须扩展测量范围。如何实现这一点？我们只需使用一个分流电阻，这样就能进行测量。

We layer large polygons. We use a multiplier resistor to expand the layering range, so that we can layer large voltages. That is all the content in our last lecture.

我们对大型多边形进行分层。利用倍乘电阻扩展分层范围，从而实现对高电压的分层。以上就是上一讲的全部内容。

Here are some photos. The first photo is a voltmeter, and the second photo is an ammeter. We use these devices to measure voltage or current.

这里有几张照片。第一张是电压表，第二张是电流表。我们使用这些仪器来测量电压或电流。

The speed is around how high the rotation speed of the object is. Actually, such a device is widely used. There are many applications where the moving-coil ammeter is applied in our real world. This board just shows some realistic photos of the device.

速度大致取决于物体的旋转速度有多高。实际上，这类装置被广泛使用。在现实世界中，动圈式电流表有许多应用场景。这块板上展示的是该装置的一些真实照片。

This is the component inside the moving coil meter. Just like we have mentioned in the slides, there is a magnetic field. The cylinder is the magnet, the magnetic field. And there is a moving coil inside. Once there is a current flowing in the moving coil, it will make the pointer rotate. Then you can see how large the current is, or how large the voltage is.

这是动圈式仪表内部的组件。正如我们在幻灯片中提到的，这里有一个磁场。圆筒是磁铁，即磁场。内部有一个可动线圈。一旦有电流流过可动线圈，它就会使指针旋转。这样你就能看出电流有多大，或者电压有多大。

It gives you the volume — for the volume of the washing. The car, for the volume of the washing machine. Yeah, you probably have a driver's license. If you have ever been driving a car, there is also this kind of display. This kind of display in a car, and they also use this kind of pointer to show how high it is.

它给你提供音量反馈——用于洗衣机的音量。汽车，用于洗衣机的音量。是的，你可能有驾照。如果你曾经开过车，那里也有这种显示屏。汽车里的这种显示屏，他们还使用这种指针来显示高度。

Apart from the moving coil ammeter, we also introduced the control system. What is the control system? How can we interpret it?

除了动圈式电流表之外，我们还介绍了控制系统。什么是控制系统？我们如何解读它？

A control system is usually described as a cascading of blocks. This means there are multiple blocks. In this image, you can see there are three blocks. So this is a cascading of blocks. And each block has its own modifying effect on the input signal.

控制系统通常被描述为级联的方块图。这意味着存在多个方块。在这张图中，你可以看到有三个方块。这就是方块的级联。每个方块对输入信号都有其自身的修改作用。

For example, for the first block, it is a transducer. This block tries to convert the physical quantity into an electrical signal. So the first block has its own modifying effect on the inputs.

例如，第一个模块是一个传感器。该模块试图将物理量转换为电信号。因此，第一个模块对输入具有自身的调制作用。

The input block converts the input into an electrical signal. The second block is the signal conditioner, which modifies the electrical signal into a conditioned signal. Finally, you have the recorder. The recorder tries to convert the conditioned signal into output movement. We have introduced different blocks in the control system, and each block has a modifying...

输入模块将输入转换为电信号。第二个模块是信号调节器，它将电信号修改为调节后的信号。最后是记录仪，记录仪尝试将调节后的信号转换为输出运动。我们已经介绍了控制系统中的不同模块，每个模块都有一个修改……

The modifying effect of each block can be defined as a gain. Each block has a gain, and they are represented by a simple K. The blocks in the previous slides can also be written in this form: each block has a gain.

每个模块的修正效应可以定义为增益。每个模块都有一个增益，用一个简单的 K 来表示。前面幻灯片中的模块也可以用这种形式来书写：每个模块都有一个增益。

Gains can be multiplied together to compute the system sensitivity. When you multiply the gains together, you get the system sensitivity. Here is an important definition: what is the transfer function? The transfer function is defined as the ratio between the output and the input.

增益可以相乘来计算系统灵敏度。当你将增益相乘时，就得到了系统灵敏度。这里有一个重要的定义：什么是传递函数？传递函数定义为输出与输入之比。

As the ratio between output and input, θ_o is the output, θ_i is the input. So θ_o divided by θ_i is the transfer function. It can be exactly expressed by the product of gains. But sometimes the control system is open-loop. Open-loop means the output cannot affect the input.

作为输出与输入的比值，θ_o 是输出，θ_i 是输入。因此 θ_o 除以 θ_i 即为传递函数。它可以精确地表示为各环节增益的乘积。但有时控制系统是开环的。开环意味着输出无法影响输入。

Open-loop control system. This means the output cannot affect the input. In this example, you can see the T point: the output is not used to modify the input. This is the definition and the property of an open-loop system — the output is not used to modify the input at all. The output will not affect the input.

开环控制系统。这意味着输出不能影响输入。在这个例子中，你可以看到T点：输出不用于修改输入。这就是开环系统的定义和特性——输出完全不用于修改输入。输出不会影响输入。

There is no feedback from the output to the input to provide corrective action if needed. Here is an example: an open-loop system controlling the speed of a direct-current motor.

输出端没有反馈到输入端以在需要时提供纠正动作。举一个例子：一个控制直流电机转速的开环系统。

In an open-loop system controlling the speed of a DC motor, if you increase the load, the speed of the motor will decrease because there is no feedback. If you want to maintain the speed, you must use a closed-loop system. In the open-loop, there is no feedback, so we cannot make any change to the input, and the output speed will decrease. Here is the closed-loop system. Compared to the open-loop, you can see there is a block.

在开环系统中控制直流电机转速时，如果增大负载，电机转速会下降，因为没有反馈。如果想要维持转速，就必须使用闭环系统。在开环中，没有反馈，因此我们无法对输入做任何改变，输出转速就会下降。这里是闭环系统。与开环相比，可以看到有一个方块。

At the bottom, which is exactly used for the feedback. So the output will be used to correct the input, or the output will be used to change or modify the input. So the output can affect the input. It is possible for the controller output to alert the input if the output changes from the desired value.

在底部，这正是用于反馈的部分。因此，输出将被用来修正输入，或者说输出将被用来改变或调整输入。所以输出可以影响输入。当输出偏离期望值时，控制器的输出有可能向输入发出警报。

If you increase the load on the output, in an open-loop system, the output speed will decrease. But in a closed-loop system, you can compensate for the reduction in shaft speed by, for example, increasing the current in the input, so that you can maintain the speed.

如果你增大输出端的负载，在开环系统中，输出转速将会下降。但在闭环系统中，你可以通过例如增大输入电流来补偿轴转速的降低，从而维持转速不变。

You can maintain the speed of the outputs. The output speed will not be decreased. If you know the output speed is decreased, then you use a feedback element to change the input—for example, by providing larger current for the input—so that the output speed will not be decreased. Because now you have a feedback system, you can change the input based on the output.

你可以维持输出的速度，使输出速度不会下降。如果你知道输出速度下降了，那么你就使用反馈元件来改变输入——例如，为输入提供更大的电流——从而使输出速度不会下降。因为现在你有了反馈系统，你可以根据输出来改变输入。

A closed-loop system actually includes four main components. The first is the input signal. The input signal is also defined as the reference signal. It is called the reference signal because we have the feedback component. The feedback will be used to compare the output with the input.

闭环系统实际上包含四个主要组成部分。第一个是输入信号。输入信号也被定义为参考信号。之所以称为参考信号，是因为我们有反馈环节。反馈将用于将输出与输入进行比较。

It is also defined as a reference. We come here: how the output is deviated from the input. The input is defined as the intended condition for the output, so it is a reference. And we have the output signal. The output is the final value that has been taken place. Output represents a measurement of the outcome achieved.

它也被定义为参考量。我们来看这里：输出如何从输入发生偏差。输入被定义为输出的预期条件，因此它是一个参考量。然后我们有输出信号。输出是已经发生的最终值。输出代表对所达成结果的度量。

This is a feedback signal, and this is the variable we are trying to control. There is a comparator. This is important — a comparator — because we want to understand how big the difference is between the output signal and the input signal. We need the comparator to give us the error. When you go back to the previous slide, this circle is exactly the comparator.

这是一个反馈信号，而这是我们试图控制的变量。这里有一个比较器。比较器非常重要，因为我们想要了解输出信号与输入信号之间的差异有多大。我们需要比较器来给出误差。回到上一张幻灯片，这个圆圈正是比较器。

This is the comparator. It will compare the output with the input and determine the error. This is the comparator. And also finally we have the controller. So based on the error—how big the error is—if you just have a very small error, we don't have to change the output a lot. But if you have a big error, you should change the output.

这是比较器。它将输出与输入进行比较，并确定误差。这是比较器。最后我们还有控制器。根据误差的大小——如果误差非常小，我们不需要对输出做很大的调整；但如果误差很大，你就应该改变输出。

The function of the controller is to generate the output signal based on the error, and try to drive the system output so that it matches the input signal. Here you can see the four components. We have the input signal θi, the output signal θo, the comparator — this circle — and the control system. These two blocks are the control system.

控制器的功能是根据误差生成输出信号，并驱动系统输出使其与输入信号匹配。这里可以看到四个组成部分：输入信号θi、输出信号θo、比较器——即这个圆圈——以及控制系统。这两个模块就是控制系统。

And each block has a gain. The feedback system also has a gain, and we use the symbol H to represent the gains in the feedback component. But in this case, how can we determine the transfer function? We know the transfer function is defined as the ratio between the output and the input. So how can we determine C(s)?

每个方框都有一个增益。反馈系统也有一个增益，我们用符号 H 来表示反馈环节的增益。但在这种情况下，我们如何确定传递函数？我们知道传递函数定义为输出与输入之比。那么，我们如何求 C(s)？

θo divided by θi. This type of system has a gain G. So θo equals G times the error. This is what you get based on the first block. The error is the difference between the input signal and the output signal after the feedback. The feedback block also has a gain H. So H times θo is the signal to the comparator.

θo除以θi。这类系统具有增益G。因此θo等于G乘以误差。这是根据第一个方框得到的结果。误差是输入信号与经过反馈后的输出信号之间的差值。反馈方框也具有增益H。因此H乘以θo是送往比较器的信号。

This is similar to a comparator. θi minus h times θo is the error we can get. If you change the form of these two equations a little bit, how do you get the transfer function for the closed-loop system?

这类似于一个比较器。θi 减去 h 乘以 θo 就是我们能得到的误差。如果对这两个方程的形式稍作变换，如何得到闭环系统的传递函数？

We have θ₀ equals the gain times the error. This is the first equation we can derive. The error is defined as the difference between the input and the output after feedback.

我们有 θ₀ 等于增益乘以误差。这是我们可以推导出的第一个方程。误差定义为输入与反馈后输出之间的差值。

This is the input minus h. Theta o is the output. We just change the form a little bit. Because e can also be expressed by theta o divided by g. And here equals to theta i minus theta o.

这是输入减去h。θo是输出。我们只是稍微变换一下形式。因为e也可以表示为θo除以g。而这里等于θi减去θo。

We change the form a little bit. θ_o equals θ_i minus h·θ_o, times g. To solve for θ_o, we get (1 + hg)·θ_o = g·θ_i. The transfer function is the ratio between the output and the input. Therefore, θ_o divided by θ_i should be g over 1 + hg.

我们对表达式稍作变形。θ_o 等于 θ_i 减去 h·θ_o，再乘以 g。求解 θ_o，得到 (1 + hg)·θ_o = g·θ_i。传递函数是输出与输入之比。因此，θ_o 除以 θ_i 应等于 g 除以 1 + hg。

G divided by 1 plus HG. Finally, you get this equation: G divided by 1 plus HG. So this is the transfer function for the closed-loop system. And sometimes, if an input is applied to a real physical system...

G 除以 1 加 HG。最终你得到这个方程：G 除以 1 加 HG。这就是闭环系统的传递函数。有时候，如果对一个实际物理系统施加输入……

The input signal is not responded to immediately. This means there is some delay—the output will not change immediately when you change the input. Why does this happen? The delay can range from a few milliseconds to a few minutes, so the range is actually quite large. Sometimes the delay is quite short, and sometimes it is quite large. If we consider how a closed-loop system responds to a step change at the reference point, we can split the time response into two time intervals.

输入信号不会立即得到响应。这意味着存在一定延迟——当你改变输入时，输出不会立即发生变化。为什么会这样？延迟的范围可以从几毫秒到几分钟不等，因此这个范围实际上相当大。有时延迟很短，有时则相当长。如果我们考虑闭环系统对参考点的阶跃变化如何响应，可以将时间响应划分为两个时间段。

The first interval is the transient period, and the second is the steady-state period. Here you can see the transient period, which means the output is not stable; it changes with time. Then there is the steady-state period, which means the output signal is almost stable. Given an input, the output does not rise to the stable value directly, but instead goes through a process.

第一个区间是瞬态周期，第二个是稳态周期。这里可以看到瞬态周期，意味着输出不稳定，它随时间变化。然后是稳态周期，意味着输出信号几乎稳定。给定一个输入，输出不会直接上升到稳定值，而是经历一个过程。

The process slowly increases and then reaches a stable value. And here we have two different output forms, depending on your control system. If your control system has very large damping behavior, which means the increase is very slow and smooth because you have very large damping. But if your control system has very small damping, the output signal will be—

过程缓慢增加，然后达到稳定值。这里我们有两种不同的输出形式，取决于你的控制系统。如果你的控制系统具有非常大的阻尼行为，这意味着增加过程非常缓慢且平滑，因为阻尼非常大。但如果你的控制系统阻尼非常小，输出信号将会是——

Oscillating. So you are overshooting, then undershooting, then overshooting, then undershooting, until finally you reach the desired output. But the output has a quicker response; it changes very quickly. And the output is underdamped, so it has oscillatory behavior. And it can reach the steady-state value quicker.

振荡。也就是说，输出先超调，再欠调，再超调，再欠调，如此反复，直到最终达到期望输出。但输出的响应更快，变化非常迅速。而且输出是欠阻尼的，因此具有振荡特性。它能够更快地到达稳态值。

This is a different case. Let us consider high damping, where alpha equals one. The control system for alpha equals one has very high damping behavior, so it reaches its designed output very slowly. For control systems, we can actually classify them into two types. The first type is regulator. The second type is servos. So there are two types of control systems: regulator and servos.

这是另一种情况。我们来考虑高阻尼的情形，即 alpha 等于 1。当 alpha 等于 1 时，控制系统具有非常高的阻尼特性，因此它达到设计输出的速度非常慢。对于控制系统，我们实际上可以将它们分为两类。第一类是调节器（regulator）。第二类是伺服系统（servos）。所以控制系统有两种类型：调节器和伺服系统。

In a regulator, the reference input is a constant value. The goal is that the output should remain constant in the face of disturbance. The input is constant and the output should also remain constant even though there is disturbance in the input. For example, a power supply should have a constant output voltage even if the output current varies significantly.

在稳压器中，参考输入是一个恒定值。目标是使输出在扰动面前保持恒定。输入是恒定的，即使输入中存在扰动，输出也应保持恒定。例如，电源应具有恒定的输出电压，即使输出电流发生显著变化。

This is exactly what we have used in your socket. For example, you plug your laptop into the socket, right? And sometimes you plug in another laptop. So the load changes. The current changes, but the output voltage is always 220. It doesn't matter how many devices you have plugged into the socket. The output voltage should be constant, even though the output current can be varied. In the servo, which means the reference input...

这正是我们在插座中已经使用的原理。例如，你把笔记本电脑插到插座上，对吧？有时候你又插上另一台笔记本电脑。于是负载发生了变化，电流也随之变化，但输出电压始终是220伏。无论你在插座上插了多少设备，输出电压都应保持恒定，即使输出电流可以变化。在伺服系统中，这意味着参考输入……

The reference is the input, right? So the reference is time-varying; it is not a constant value anymore. It is time-varying. And the objective is that the output should track the input with a small error. So if the input has a form like this, the output should also try to mimic the input. They should have the same shape. The goal is to track the input with a very small error. And here is an example: a radar dish tracking a target, or a robot following a very complex trajectory in 3D space.

参考信号就是输入，对吗？所以参考信号是时变的，它不再是一个常数值，而是随时间变化的。目标是让输出以很小的误差跟踪输入。如果输入具有这样的形态，输出也应当尝试去模仿输入，二者应具有相同的形状。目标就是以非常小的误差跟踪输入。这里举一个例子：雷达天线跟踪目标，或者机器人在三维空间中跟随一条非常复杂的轨迹。

Once a trajectory is given, what you want the robot to do is follow this trajectory. If you have a robot navigating a room with obstacles here and the robot is here, and it has to navigate, once you determine the trajectory, this is the trajectory the robot should follow. The robot should try to follow this trajectory with very small deviation. Any questions at that point?

一旦给定了一条轨迹，你希望机器人做的就是跟随这条轨迹。假设有一个机器人在一个房间里导航，这里有障碍物，机器人位于此处，它需要进行导航。一旦你确定了轨迹，这就是机器人应当跟随的轨迹。机器人应当尝试以非常小的偏差来跟随这条轨迹。到这里有什么问题吗？

Great. That's a basic introduction for...

很好。这是一个关于……的基本介绍。

This is a basic introduction to control systems. Now we can see some real photos of control systems. Control systems are actually widely used in our daily life. In many of the products, we can see control systems. For example, the car is actually a very complex system. It includes a lot of control systems. You have the engine, and you have to control the engine—how high the speed of the engine should be. And you also have the braking system. When you drive too fast, the braking system kicks in.

这是控制系统的基本介绍。现在我们可以看一些控制系统的实际照片。控制系统实际上在我们的日常生活中被广泛使用。在许多产品中，我们都能看到控制系统。例如，汽车实际上是一个非常复杂的系统，它包含许多控制系统。你有发动机，你必须控制发动机——发动机的转速应该多高。你还有制动系统。当你开得太快时，制动系统就会介入。

We also have a control system for the battery. The battery management system controls when to charge the battery and when to discharge it. Its purpose is to save the battery and increase your driving kilometers if you use an electric vehicle. Similar to the car, the airplane is also very complex. We have many control systems in the aircraft. Here you can see some other photos.

我们还有一个电池控制系统。电池管理系统控制何时为电池充电以及何时放电，其目的是保护电池，如果你使用电动汽车，还能增加行驶里程。与汽车类似，飞机也非常复杂，我们在飞行器中有很多控制系统。这里你可以看到一些其他照片。

For humanoid robots or legged robots, when they walk, you have to control how they should walk. For the ship, the autonomous ship system—the ship autopilot—is a kind of autonomous system. When you have an autonomous ship, it can navigate autonomously on the surface of the sea. This autopilot control system is also a kind of control system. So here you can see that control systems can be found in many applications.

对于人形机器人或足式机器人，当它们行走时，你必须控制它们应该如何行走。对于船舶而言，自主船舶系统——即船舶自动驾驶仪——是一种自主系统。当你拥有一艘自主船舶时，它可以在海面上自主航行。这种自动驾驶控制系统也是一种控制系统。因此，我们可以看到控制系统广泛应用于许多领域。

Lecture 5 is just a basic introduction of the moving coil meter: how to measure current, how to measure voltage. We also introduced the control system—how the control system looks like for an open loop and for a closed loop. So these are the two things covered in Lecture 5.

第五讲仅是对动圈式仪表的基本介绍：如何测量电流、如何测量电压。我们还介绍了控制系统——开环和闭环控制系统分别是什么样的。这就是第五讲所涉及的两个内容。

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