It has been verified that there were examples of automation in ancient times, but automatic control in the modern sense began with Watt's steam engine. It is said that newcomen invented the steam engine before Watt, but the speed control problem of the steam engine has not been solved, so that the speed will soar, the machine will be damaged and a big accident may occur. Watt installed a small stick on the shaft of the steam engine. One end of the stick is connected with the steam release valve. When the steam release valve is released, it will close and the speed will increase. Pressing the valve will open and the speed will decrease; At the other end of the stick is a small heavy hammer, and somewhere in the middle of the stick is connected with the rotating shaft through a fulcrum. When important official rotates, the stick will swing due to centrifugal force. If the rotating speed is too high, the stick will swing very high, and when the steam release valve is pressed down, the rotating speed will decrease; The speed is too low to swing the stick. Loosen the steam release valve and close it, and the speed will increase. In this way, the steam engine can automatically maintain a stable speed, which not only ensures safety, but also is convenient to use. It is because of this small governor that Watt's name is associated with the Industrial Revolution, and newcomen's name will also appear in the history books.
There are many similar examples in mechanical systems, and the necessary toilet at home is another example. After flushing, the water level of the water tank drops, the float drops with the water level, and the water inlet valve opens. As the water level rises, the water inlet valve is gradually closed until the water level reaches the specified height, and the water inlet valve is completely closed, and the water in the water tank is just available for next use. This is a very simple but ingenious water level control system, a classic design, but it is not easy to analyze it with classic control theory, but it is beside the point.
These mechanical systems are ingenious in design and reliable in work, which is really wonderful. But in practice, if you need such creative thinking every time, it will be too tired. It is better to have a systematic method to solve the problem of "full" automatic control, which is the origin of control theory.
Adults have taught us to watch the road when we are young. Why? I don't know if I took a wrong turn without looking at the road, so I bumped into each other. What if you look at the road? If you go wrong, you will see it immediately. Quickly adjust your steps and get back on track. Here is the first important concept in automatic control: feedback.
Feedback is a process:
1. Setting goals is the direction for children to follow the example of walking.
2, measuring the state, the child looks at the road, that is, measuring his own direction.
3. Compare the measured state with the set goal, and compare the forward direction seen by the eyes with the forward direction in the mind to judge whether the forward direction is correct; If not, what's the difference?
4, adjust the action, in the mind according to the deviation of the actual direction and set goals, decided to adjust the amount.
5, the actual implementation, that is, the actual movement, back to the right direction.
In the whole process of walking, this feedback process is repeated, so that the child will not stagger. However, there is a problem here: if everything happens at the same time in an instant, then this feedback process will not work. For feedback to work, there must be a certain reaction time. Fortunately, everything in the world has a process, which buys the time needed for feedback.
The feedback process is also called closed-loop process. Since there is a closed loop, there is an open loop. Open loop is a control process without feedback. Set a control function, and then execute it, without correction according to the actual measured value. Open-loop control is only effective for simple processes, such as timing control of washing machines and dryers. How clothes are washed and dried depends entirely on the initial settings. For problems such as washing machines and dryers, it is good to set up a little more time, which is a bit wasteful, but it can ensure the effect. For air conditioners, we can't simply set a cycle of turning on 10 minutes and turning off for 5 minutes regardless of the room temperature, but we should carry out closed-loop control according to the actual temperature, otherwise the indoor temperature will reach God knows. I remember reportage was very popular in the 1980s. Xu Chi wrote Goldbach's conjecture, so people all over the country are vying to be scientists. Novelists are also scrambling to write about scientists, and their achievements are too small. So it is not surprising that some people have written "fast tracking without feedback". I was eating bricks at the university, and I was very interested in this new scientific discovery. I read it from beginning to end, and I don't understand how to track it quickly without feedback. Now think about it, the novel is a novel, but this unscrupulous writer is ridiculous. Without feedback, he had to follow, without looking at the target or where he had gone. What are the traces? It's almost like a perpetual motion machine. Why not choose a better topic, cold fusion or something? At least in theory, it is still possible. That's beside the point
Mathematically, the dynamic process is described by a differential equation, and the feedback process is to establish a relationship between the input term and the output term of the differential equation describing the dynamic process, thus changing the original properties of the differential equation. It is in this feedback and dynamic process that automatic control makes a fuss.
The air conditioning in the room is a simple control problem. However, this only refers to a single room, and the central air conditioning problem of all rooms in the whole high-rise building is actually a complicated problem, which is beyond the scope of discussion here. The indoor temperature is set at 28 degrees in summer, and the actual temperature is higher than 28 degrees. The air conditioner began to cool down, reducing the indoor temperature. When the actual temperature is lower than 28 degrees, turn off the air conditioner and the room temperature will naturally rise due to the ambient temperature. With such a simple switch control, the indoor temperature should be controlled at 28 degrees. However, there is a problem here. When the temperature is slightly higher than 28 degrees, the air conditioner will start. Below 28 degrees, the air conditioner is turned off; Then, if the temperature sensor and the switch of the air conditioner are sensitive enough, the switching frequency of the air conditioner can be infinitely high, and the air conditioner will be constantly turned on and off, which is not good for the machine and unnecessary in practice. The solution is to set a "dead zone", which is turned on when the temperature is higher than 29 degrees and turned off when it is lower than 27 degrees. Be careful not to do it backwards, or the control unit will go crazy.
With the dead zone, the indoor temperature can no longer be strictly controlled at 28 degrees, but "swing" between 27 and 29 degrees. If the ambient temperature is constant and the cooling capacity of air conditioner is constant, the period of temperature "sloshing" can be calculated by knowing the dynamic model of indoor heating/cooling. But since it's a story, I won't bother about it.
This kind of switch control looks "earthy", but in fact it has many benefits. For most processes, the accuracy of switch control is not high, but it can ensure stability, or the output of the system is "bounded", which means that the actual measured value will be limited to a certain range and it is impossible to spread indefinitely. This stability is different from the so-called asymptotic stability emphasized in general control theory, and is called BIBO stability. The former requires the output to be set in the final trend, while the latter only requires the output to be bounded under the action of bounded input. BIBO refers to bounded input and bounded output.
For simple processes with low precision requirements, this kind of switch control (or relay control, because the earliest control method is realized by relay or electromagnetic switch) is enough. But in many cases, the control of this "total estimation" can not meet the requirements. The car is driving on the expressway, and the speed is set at constant speed cruise control. If the speed goes down a few kilometers, I feel that I have suffered, but if I go up a few kilometers, I will be arrested by the police and issued a ticket. Whose is this?
On-off control is discontinuous control, the control effect is "full dose" when increasing, and "full dose" when decreasing, with no intermediate transition. If the cooling capacity of air conditioner has three settings, namely, small, medium and large, the control accuracy of room temperature can be greatly improved, in other words, the "shaking" range of temperature will be greatly reduced. Then, if there are more air conditioners, from small to medium to large, will the control accuracy be higher? Yes, in that case, why not use stepless air conditioning? Isn't it possible to control the room temperature more accurately? be
Stepless or continuously adjustable air conditioners can accurately control the temperature, but switch control is no longer available. In domestic air conditioners, continuous adjustment is not the majority, but hot water shower is a typical continuous control problem, because the faucet can continuously adjust the water flow. When taking a bath, it is assumed that the cold water faucet remains unchanged and only hot water is adjusted. The temperature is high, so turn down the hot water. The temperature is low. Turn on the hot water. In other words, the control function should change in the direction of reducing the control deviation, which is called negative feedback. The control direction is right, and there is a problem of control quantity. High temperature 1 degree. How much should the hot water be turned down?
Experience tells us that according to the specific faucet and water pressure, the temperature is 1 degree, and the hot water needs to be turned down by a certain amount, such as one grid. In other words, the control quantity is proportional to the control deviation, which is the classic law of proportional control: control quantity = proportional control gain * control deviation, and the greater the deviation, the greater the control quantity. Control deviation is the difference between the actual measured value and the set value or target value. Under the law of proportional control, the deviation is reversed and the control quantity is reversed. That is to say, if the shower water temperature is required to be 40 degrees, and the actual water temperature is higher than 40 degrees, the hot water faucet will change to the closing direction; When the actual water temperature is lower than 40 degrees, the hot water faucet changes its opening direction.
However, the proportional control law cannot guarantee that the water temperature can reach 40 degrees accurately. In real life, people fine-tune the hot water faucet at this time. As long as the water temperature is not suitable, they will adjust it bit by bit until the water temperature is suitable. This control law, which is gradually fine-tuned as long as the control deviation does not disappear, is called integral control law in control, because the control quantity is directly proportional to the accumulation of control deviation in time, and its proportional factor is called integral control gain. The reciprocal of the gain of integral control is commonly used in industry, which is called the integral time constant. Its physical meaning is the time required to double the control quantity when the deviation is constant. It should be noted that whether the control deviation is positive or negative depends on whether the actual measured value is greater than or less than the set value, so as long as the control system is stable, that is, the actual measured value will eventually stabilize at the set value, the accumulation of control deviation will not be infinite. Here again, the basic function of integral control is to eliminate the residual of control deviation (also called residual).
Proportional and integral control laws can deal with a large class of control problems, but they are not without room for improvement. If the water temperature of the water pipe changes rapidly, people will adjust the hot water faucet according to the change of water temperature: with the increase of water temperature, the hot water faucet changes to the closing direction, and the faster the temperature rises, the more it is opened; When the water temperature drops, the hot water faucet changes its opening direction. The faster the temperature drops, the more it shuts down. This is the so-called differential control law, because the control quantity is proportional to the change rate of the actual measured value, and its proportional factor is called proportional control gain, which is also called differential time constant in industry. Differential time constant has no specific physical meaning, but integral is called time constant, so is differential. The focus of differential control is not the specific value of the actual measured value, but its changing direction and speed. Differential control has many advantages in theory and practice, but its limitations are also obvious. If the measured signal is not very "clean" and there is a little "burr" or disturbance from time to time, then the differential control will be confused by these troubles and produce many unnecessary or even wrong control signals. Therefore, it is very cautious to use differential control in industry.
Proportional integral differential control law is the most commonly used control law in industry. People generally call it PID control according to the English abbreviation of proportional-integral-differential. Even today when more advanced control laws are widely used, various forms of PID control still account for more than 85% of all control loops.
In PID control, the characteristic of integral control is that as long as there is residual error (that is, residual control deviation), integral control will gradually increase the control function until the residual error disappears. Therefore, the effect of integration is relatively slow, except in special circumstances, as a basic control function, it is slow and not urgent. The characteristic of differential control is that although the actual measured value is lower than the set value, its rapid rising momentum needs to be restrained as soon as possible, otherwise it will be too late to react when the actual value exceeds the set value, which is where differential control comes into play. As a basic control, differential control only looks at the trend, not the specific value, so the ideal situation is to stabilize the actual value, but where it is stabilized depends on your luck, so differential control cannot be used as a basic control. Proportional control does not have these problems. Proportional control has fast response and good stability, which is the most basic control function and is "skin". Integral and differential control can enhance proportional control, and are rarely used alone, so they are "gross". In practical use, proportion and integral are generally used together, proportion plays the main control role, and integral helps to eliminate residual. Only when the controlled object is slow and needs to be compensated as soon as possible at the beginning of the reaction, differential is adopted. Proportion and differentiation are rarely used.
The accuracy of continuous control is incomparable to that of switch control, but the high accuracy of continuous control comes at a price, that is, stability. The control gain determines the sensitivity of control action to deviation. Since the gain determines the sensitivity of control, wouldn't it be better to be more sensitive? Not exactly. Let's take the cruise control of a car as an example. Slow down, add a little throttle, slow down again, and then refuel. Of course, when the speed goes up, it will be the other way around. However, if the speed is lower, the throttle will increase a lot, and if the speed is lower, the throttle will be increased wildly, so that the speed will not stabilize at the required set value and it may get out of control. This is instability. Therefore, the setting of control gain is special. There are similar examples in life. The national economy is overheated and needs economic adjustment, but too much adjustment will cause a "hard landing" and recession; Stimulation is needed in a recession. Similarly, excessive stimulation can also lead to "false prosperity". To achieve a "soft landing", economic adjustment measures need to be just right. This is also a question of the stability of the economic power system.
In practice, how much gain is the most appropriate, there are many calculation methods in theory, but in practice, the best gain is usually found according to experience and debugging, which is called parameter tuning in the industry. If the system response lags behind the control function, the oscillation is large, and it is generally too integral; If the reaction of the system is neurotic and always oscillates at high frequency and small amplitude, then differentiation is generally a bit excessive. Intermediate frequency oscillation is of course a matter of proportion. However, the frequency of each system is different. What is high frequency and what is low frequency? These words are not clear. I want to respond to Chairman Mao's words: "Analyze the specific situation in detail", so I just laughed.
More specifically, there are two ways to set parameters. First debug the proportional gain to ensure basic stability, and then add the necessary integral to eliminate the residual. Only when it is most needed, such as reflecting the slow temperature process or large-capacity liquid level process, when the measurement noise is very low, add a little differentiation. This is an "academic" way, which is very effective in most cases. However, there is a "crooked road" in the industry: a very small proportion is used, but the integral function is greatly strengthened. This method is completely contrary to the analysis of control theory, but it is effective in practice. The reason is that when the measurement noise is serious or the system is allergic, the control law based on integral is relatively mild, and it is not easy to excite unstable factors, especially the high-frequency part with high uncertainty. This is also the original intention of Deng Xiaoping's "stability first".
In many cases, after the initial PID parameters are adjusted, as long as the system is not unstable or the performance is obviously degraded, it will not be re-adjusted. But what if the system is unstable? Because most practical systems are open-loop stable, that is to say, as long as the control function remains unchanged, the system response should eventually stabilize at a value, although it may not be the set value, so the first action to deal with instability is to reduce the proportional gain, according to the actual situation, 1/3, 1/2 or even more, and at the same time increase the integration time constant, which is often multiplied, and then reduced or even reduced. If there is feedforward control, it is also useful to reduce the feedforward gain appropriately. In actual operation, the system performance will not suddenly deteriorate inexplicably, and the above-mentioned "fire extinguishing" reset is often temporary. After the mechanical or raw material problems in the production process are eliminated, the parameters should be reset to the initial values, otherwise the system performance will be too lazy.
For the new factory, the system has not been put into operation, so it cannot be set according to the actual response. Usually, the initial parameters are estimated first, and the control loops are set one by one during the system operation. My own experience is that for a general flow cycle, the ratio is set at about 0.5, the integral is about 1 min, and the differential is 0. This combination is generally not a big problem at first. The temperature loop can start from 2, 5 and 0.05, the liquid level loop from 5, 10 and 0, and the air pressure loop from 10, 20 and 0. Since these are empirical estimates, it is of course necessary to analyze the specific situation, and it is impossible to be "universally applicable".
Differential is generally used for slow response systems, but there are always some exceptions. I once met a small condensate tank with a diameter of only two feet and a length of only five feet, but the flow rate was 8- 12 ton/hour. When a fault occurs, the liquid level changes very quickly. No matter how to adjust the proportion and integral, it is difficult to stabilize the liquid level. Usually, the control valve has just started to react and the liquid level has reached the top or bottom. Finally, the differential of 0.05 is added. As soon as the liquid level changes, the control valve begins to restrain, but it stabilizes. This is contrary to the conventional parameter setting method, but in this case, it is the "only" choice, because the measured value and the saturation of the control valve become the main problems of stability.
Let's talk a few more words about the practice of industry taking integral as the leading control role. Academically, the stability of control is basically asymptotically stable. In the case that there is no way to prove asymptotic stability, Bi Bo stability is "suboptimal" and not very popular. There are two seemingly similar but essentially different aspects of stability in industry: one is of course asymptotic stability, and the other is stability, but it does not necessarily converge to the set value, or stability takes precedence over convergence. Specifically, it is necessary to stabilize the system at a value and not to move around, but it is not too important not to set a value, as long as it is not too outrageous. There are many examples For example, the pressure of the reactor is an important parameter. If the reactor is unstable, the feed ratio of raw materials will be disordered, the feed of catalyst will be unstable and the reaction will be unstable. But it doesn't matter much whether the pressure of the reactor is 10 atmosphere or 12 atmosphere, as long as it moves slowly but steadily to the set value. This is rarely involved in control theory, and it is also an important reason why integral dominant control is often used in industry.
As mentioned above, the frequency of the system is originally the frequency when the system responds to continuous oscillation, but there are three kinds of people in the control field: one is electrician characterized by electromechanical power system, including aviation and robots, the other is chemical engineer characterized by continuous process, including metallurgy and papermaking, and the other is applied mathematics characterized by stability of differential equations. In the era of Watt and Toilet, it was peaceful to fight on their respective hills and stay out of it. However, after the control rose from art to theory, there were always people who liked "unification", and electricians helped to grab the first place and put good control theory into the electrician's frequency. Guys, that's not a frequency, that's a ... complex frequency. Since those abnormal electricians (alas, the deer kick really came) can churn out virtual electricity and complex frequencies, forget it, but they just hurt innocent people like us and were forced to suffer this mental torture.
The reason is the stability of the system. As mentioned above, if the parameters of PID are not set properly, the system may be unstable. Besides groping, is there any way to calculate the appropriate PID parameters theoretically? As mentioned earlier, the dynamic process can be described by differential equations. In fact, in PID stage, this is only a very narrow branch of differential equation: linear ordinary differential equation with one variable. If you remember the high number of your freshman year, you must remember the linear ordinary differential solution. In addition to the method of separating variables, if the independent variable time is expressed by t, the most common solution is to substitute exp(λt) into the differential equation, and then the solution becomes the characteristic equation of λ algebraic equation. If the solution can be a real number or a complex number, then use trigonometric function to expand it (anyway, the nightmare feeling of freshman is not found at all). As long as the real roots are negative, the differential equation is stable, because the negative exponential term eventually converges to zero, and it doesn't matter how many complex roots there are, which has no effect on stability. However, it is still not easy to solve and analyze this problem, which is still beyond the scope of "concrete analysis of specific situations" and it is difficult to draw a general conclusion.
The root trajectory is still polite, and there are more abnormal Nyquist, Byrd and Nichols methods, and the brain is wide open. It's all those electricians. Nowadays, computer analysis has become very popular, and the classic graphic analysis still has enduring charm, because graphic analysis not only tells you the dynamic response parameters such as whether the system is stable or unstable, but also qualitatively tells you the closed-loop performance changes caused by gain changes and even system parameter changes. Hey, weren't you just talking about a pervert? Well, perverts have perverted charm, don't they? Ha ha.
The control theory characterized by frequency analysis (also called frequency domain analysis) is called classical control theory. Classical control theory can analyze the stability of the system, but there are two preconditions: first, we must know the mathematical model of the controlled object, which is not easy to obtain in practice; Second, the mathematical model of the controlled object will not change or drift, which is difficult to do in practical operation. Differential equations can be established for simple processes, but the control of simple processes is not troublesome, and the parameter adjustment of empirical methods is not that troublesome. However, for the loop that really needs theoretical calculation, it is too difficult to establish the model, or the uncertainty of the model itself is high, which makes the theoretical analysis meaningless. Classical control theory has been successfully applied in the fields of machinery, aviation and motor. After all, from F=ma, the dynamic models of all mechanical systems can be established, the weight of iron bumps will not change inexplicably, and the main environmental parameters can be measured. However, the successful application of classical control theory in chemical control is at least rare. I'll give you a 50-plate distillation column, with one gas phase feed and one liquid phase feed. There are side outlets at the top and bottom of the tower, and the air-cooled condenser at the top and reboiler at the bottom of the tower are both equipped with intermediate reboilers, which can be modeled slowly. When the model was established, the air-cooled condenser was affected by wind, frost, rain and snow, the high-pressure steam pressure in the reboiler was affected by the friendly device, the temperature and saturation of gas phase feed were changed by the upstream device, and the mixed composition of liquid phase feed was changed by the upstream device, but the composition could not be changed.
Goethe, an old guy, said 200 years ago that theory is gray and the tree of life is evergreen. We know that red deer likes gold or silver, or at least red, but we have to make do with green. In practice, PID has many cousins, helping big cousins to fight the world together.
Proportional control is characterized by large deviation and great control effect. However, in practice, this is sometimes not enough. Large deviation and large proportional gain. Further strengthen the correction of large deviation and pull the system back to the set value as soon as possible. When the deviation is small, of course, there is no hurry, just take it slowly, so that the gain is small and the stability is strengthened. This is the origin of double gain PID (also known as dual-mode PID). It's right to think about it. Aiming anti-aircraft guns at enemy planes is a control problem. If the barrel is still pointing away from the target angle, first turn the barrel near the target angle as soon as possible, and the action should be fierce. But the gun bore refers to a place close to the target, so aim slowly and carefully. There are many similar problems in industry. A special case of double gain PID PID with dead zone, when the deviation is small, the gain is zero, that is, when the measured value is not much different from the set value, it is left unchecked without control. This is widely used in liquid level control of large buffer vessels. Originally, the buffer container was used to buffer the flow change, so it doesn't matter where the liquid level is controlled, as long as it is not too high or too low. However, the flow from the buffer container to the downstream device should be as stable as possible, otherwise the downstream device will be unnecessarily disturbed. Dead-time PID is most suitable for this kind of control problem. But there is no such thing as a free lunch. The premise of dead zone PID is that the liquid level will "automatically" stabilize in the dead zone. If the dead zone is improperly set or the system is often disturbed, the "out of control" state in the dead zone will cause the liquid level to "advance" to the boundary of the dead zone indefinitely. Finally, when it enters the "controlled" area, the control will be over-controlled, and the liquid level will "advance" in the opposite direction indefinitely. The end result is that the liquid level will always oscillate at both ends of the dead zone, but it will never be stable. Hit what? Deer hunting? )。 Double gain PID has the same problem, but it is better than dead zone PID. After all, there is only the difference between "strong control" and "weak control", and there is no "no control zone". In practice, the difference between the internal and external gains of double gain is less than 2: 1, and it is not meaningful. If it is greater than 5: 1, we should pay attention to the above-mentioned problem of continuous oscillation or oscillation.
The problem of double gain or dead zone PID is that the change of gain is discontinuous, and the control action suddenly changes on the dead zone boundary, which is easy to induce the adverse reaction of the system, but the square error PID does not have this problem. Once the error is squared, the curve of control quantity versus error becomes a parabola, which also achieves the effect of "small deviation, small gain, large deviation and large gain", and there is no sudden discontinuous gain change. But the error square has two problems: one is that when the error is close to zero, the gain is close to zero, and it returns to the dead zone PID; Second, it is difficult to control the specific shape of parabola, or it is difficult to determine where the gain turns. For the first question, a basic linear PID can be added to the error square PID, which is zero error or non-zero gain; For the latter problem, another module is needed to calculate the continuously changing gain. The details are trivial. The deviation is sent to the piecewise linearization (that is, broken line) calculation unit, and then the calculation result is output to the PID controller as proportional gain. The horizontal segments of the broken line should have different gains, and the diagonal lines connecting different horizontal segments should correspond to the continuous change of gains. The curve of variable gain can be adjusted at will by setting the vertices of horizontal and diagonal segments. If the "ambition" is bigger, adding several calculation units can make asymmetric gain, that is, the gain is low when the temperature rises and high when the temperature drops, so as to cope with the common problems of fast temperature rise and slow temperature drop in the process of temperature rise.
Double gain or error square is an article about proportional gain, and the same activity can also be used in integration and differentiation. A more extreme PID law is called integral separation PID, and its idea is: proportional control has good stability and fast response, so when the deviation is large, the integral in PID is closed; When the deviation is small, fine-tuning and eliminating residual are the main problems, so the proportional function is weakened or even turned off, while the integral function is cut into control. The concept is good, but when implemented, there are many problems of undisturbed handover.
These abnormal PID are difficult to analyze the stability of the system in theory, but they have solved many problems in practice. To be honest, these pids have been used in practice.
Complex structure PID
When fighting, if the enemy is too stubborn, either change a bigger gun and knock him down; Either adopt more ingenious tactics and stun the enemy. The same is true of control. The problem that single loop PID is difficult to solve can often be solved by more ingenious loop structure.
A single PID loop can certainly suppress the disturbance, but if the main disturbance is in the loop and it is clear, it is a very good idea to add an inner loop as an auxiliary. Remember the example of taking a hot bath? If the hot water pressure is unstable, it is always troublesome to adjust the hot water faucet for this purpose. If one person is responsible for adjusting the hot water flow according to the hot water pressure and stabilizing the hot water pressure at the calibrated value, the water temperature will be much easier to control when taking a bath. Just tell that person how much hot water flow is needed now, and don't worry about the influence of hot water pressure on hot water flow. The control loop responsible for hot water flow is the inner loop, also known as the secondary loop, while the temperature of the bathtub is the outer loop, also known as the primary loop. Of course, the primary loop commands the secondary loop, just like the automatic command mechanization and the person who learns automatic control commands the person who learns electromechanical ... Stop it, and if you go any further, you will be kicked by deer, horse, cow and donkey. This structure of main loop with secondary loop is called cascade control, which was once the first "advanced process control" after single loop PID in industry. Now cascade has been used a lot, and no one calls it "advanced process control". The main function of cascade control is to suppress the disturbance in the loop and improve the overall control performance. But cascade can't be used indiscriminately. If the speed of the main circuit is similar to that of the auxiliary circuit, or the speed of the main circuit is even slower than that of the auxiliary circuit (which can be realized through abnormal debugging), such a cascade will have problems. Theoretically, * * * vibration frequency can be used for analysis, but don't worry. If you think about it with your knees, you will know that an impatient boss has commanded a subordinate who is in a hurry to swallow saliva, and the result can only be that everyone is exhausted and things are screwed up. On the contrary, if a calm boss orders a quick subordinate, it will certainly do well.
Bring positive energy
A little thing, however, embodies the care between people and the transmission of love. It accelerates fermentation and makes us move