What control methods are included in a nonlinear parametric system

Parametric design, the architectural design as a complex system, the various influencing factors as parametric variables, and on the basis of the site and architectural research, to find the rules that connect the parametric variables, and then establish a parametric model, the use of computer software to generate building volume, space, form or structure, and by changing the fixed value of the parametric variables, to obtain a multi-solution and dynamic design scheme.

It has been said that "nonlinear architecture will become an important architectural movement in the next millennium, guided by complex science." ”

It has been said that "non-linear architecture will be a symbol of the information society and lead the new trend of world architecture in the 21st century." ”

There are countless similar introductions on the Internet, and the reading is not only tongue-twisting but also meaty, and the people who talk about it never care that their praise is exaggerated.

New architectural theories and design methods are always emerging, and it is worth watching whether they can become mainstream.

We never reject something new, but we must take it calmly after choosing, rather than passively accepting it all.

In the past 20 years, foreign design companies have flocked to China, and China has become a test field for world architecture, among which there are many classics, and there are not a few failures that cost people and money.

One method cannot be suitable for all buildings, one form cannot be suitable for all cities, and if one day, the city of Beijing is reduced to Manhattan and surrounds the Forbidden City, I wonder if the architect with such a "masterpiece" will be at ease.

It is also difficult to find a real linear system in life, there are many nonlinear controls, such as automobile power assist control, robot joint control, aircraft wire control, etc., in recent years, there has been little research on linear control, the control technology in the field of nonlinearity has developed rapidly, now there are more h infinity, sliding mode change structure, observer also has a lot, the hottest spiral sliding mode in the world at present.

The most common nonlinear characteristics: dead band characteristics, saturation characteristics, gap characteristics, relay characteristics, etc.

1) Dead zone characteristic. For a linear non-static distortion system, the steady-state error is zero when the system enters the steady state. If the controller contains a dead-time feature, when the system enters the steady state, the steady-state error may be a certain value within the dead band range, so the most direct impact of the dead time on the system is to cause the steady-state error.

2) Saturation characteristics. Generally speaking, the reduction of the equivalent gain will reduce the overshoot of the system, weaken the oscillation, and increase the steady-state error.

3) Gap characteristics. In gear transmission, due to the presence of clearance, when the direction of the driving gear changes, the driven wheel remains in place and does not change the direction of rotation until the clearance disappears.

4) Relay characteristics. The relay characteristic can make the controlled tampering manual device work at the maximum input signal, and can give full play to its Lie crack adjustment ability, so it is possible to use the relay characteristic to achieve fast tracking.

The most common non-quiet linear characteristics: dead band characteristics, saturation characteristics, gap characteristics, relay characteristics, etc.

There will be some strange phenomena that cannot occur in nonlinear systems, which can be summarized as follows: the stability and output characteristics of linear systems are only determined by the structure and parameters of the system itself. The stability and output dynamics of a nonlinear system are not only related to the structure and parameters of the system, but also to the initial conditions of the system and the size of the input signal.

For example, the motion of the system is convergent (stable) in the initial condition with a large amplitude, but divergent (unstable) in the initial condition with a small amplitude, or vice versa. The equilibrium state of motion of a nonlinear system, in addition to the equilibrium point, may also have periodic solutions.

There are two types of periodic solutions, stable and unstable, the former is unobservable, and the latter is actually observable. Therefore, in a simple nonlinear system, even if there is no external input, an oscillation with a certain amplitude and frequency will be generated, which is called self-excited oscillation, and the corresponding phase rail line is the limit loop. Changing the parameters of the system can change the amplitude and frequency of the self-oscillation.

This feature can be applied to practical engineering problems for a technical purpose.

When the input of a linear system is a sinusoidal function, the output steady-state process is also a sinusoidal function of the same frequency, which differs only in phase and amplitude. However, when the input of a nonlinear system is a sinusoidal function, its output is a non-sinusoidal periodic function containing higher harmonics, that is, the output will produce phenomena such as frequency doubling, frequency division, and frequency encroachment. Complex nonlinear systems can also produce abrupt changes, bifurcations, chaos and other phenomena under certain conditions.

The analysis of nonlinear systems is far more complex than that of linear systems, and there is a lack of effective mathematical tools that can deal with them in a unified manner. In many engineering applications, it is difficult to solve the exact output process of the system, and it is often limited to considering: whether the system is stable or not.

Whether the system produces self-oscillating oscillations (see Nonlinear Vibrations) and how to measure their amplitude and frequency. How to limit the amplitude of self-oscillation to eliminate it. For example, an oscillation of one frequency of 1 can be suppressed by an oscillation of another frequency of 1, and this asynchronous rejection phenomenon has been used to suppress the self-oscillation caused by backlash in servo systems of some heavy equipment.