The basis of self-control

The basis of self-control

1. What is the minimum phase system?
The minimum phase system is a system in which all poles and zeros are located on the left half plane of s.

2. What is the frequency response of the amplifier?
The frequency response of the amplifier is to give a sine signal to the system, and a sine signal of the same frequency will be output at the output, but it will be different from the input signal in amplitude and phase.

3. The concept of transfer function
Under zero initial conditions, the ratio of the Laplace transform of the output of a linear time-invariant system to the Laplace transform of the input is defined as the transfer function of the linear time-invariant system. The transfer function represents the inherent characteristics of the system, and is only related to the structure of the system, and has nothing to do with the input and output.

4. Briefly describe the characteristics of the PID controller, respectively explain the influence of the proportional, integral, and differential links on the system, and the design of the parameters of the PID controller?
PID control does not require an accurate model, and has a wide range of applications and strong robustness. PID corresponds to proportional, integral, and derivative control respectively.
Increasing the proportional coefficient can reduce the steady-state error and speed up the system response, but it cannot eliminate the error. If the proportional coefficient increases until the gain margin increases, the stable system will diverge.
Integral control is beneficial to eliminate steady-state errors, produce a lagging phase, increase the integral proportional coefficient, and increase system oscillation.
The addition of the differential link is beneficial to improve the dynamic performance. The differential link introduces a zero point, which will change the damping ratio of the closed-loop system, increase the system frequency band, accelerate the response speed, and reduce overshoot.
PID parameter tuning is generally based on experience: first adjust the proportion to the critical oscillation, then adjust the integral to 4:1, and then adjust the derivative.

5. What are the dynamic characteristics of the second-order system in the case of step input?
The overshoot is only related to the damping ratio ξ. In the case of underdamping, the smaller the damping ratio, the faster the response. The larger the overshoot, the more obvious the oscillation and the worse the stability. In the case of over-damping, the larger the damping ratio, the greater the response. The slower, but the better the stability. The best damping ratio is 0.707, and the combination of speed and smoothness is the best at this time.

6. Conditions for system stability? BIBO stable? Progressive and stable?
For a linear system, the stability of the system requires that all poles are on the left half plane of s. BIBO stability is not necessarily gradual stability, gradual stability must be BIBO stability.
For nonlinear systems, the stability analysis is also related to the input, and the phase plane method and the description function method are generally used for analysis.

7. The characteristics of the first-order inertial link
No vibration, no overshoot

8. The concept of stability? The concept of steady-state error? What is the relationship between the two? Under a certain input signal, the steady-state error is infinite, does it mean that the system is unstable?
Stability refers to the ability of the system to recover from the initial deviation state to the equilibrium state after the disturbance disappears. The steady-state error occurs only when the system is stable. The steady-state error is infinite, which means that the system cannot track the input signal, and it cannot explain the instability
supplementary problem: a system's step response is stable, then is this system a stable system?
For a linear time-invariant system, the definition of stability is that when the input is an ideal pulse, the system output can finally return to the equilibrium point. It seems that the step response is stable. My understanding is that the linear time-invariant system satisfies the principle of superposition, and the step response can be regarded as With the superposition of countless impulse responses, the impulse response will generate an impulse and then tends to 0, and the unit step response corresponds to an output stable at 1. For nonlinear systems, stability is related to the input.

9. The reason why lag/lead tandem correction can improve system performance?
The lag correction acts on the low frequency band, which can reduce the cut-off frequency and increase the phase margin; the lead correction can increase the cut-off frequency, speed up the system response, increase the phase margin, and improve the system stability.

10. What performance of the control system are affected by the various frequency bands of the open-loop amplitude-frequency characteristics of the control system?
Low frequency band: affects whether the system produces errors and the magnitude of the steady-state error (this is because the low frequency band is mostly some integration links, which affect the steady-state error)
Middle frequency band: affects the stability of the system, the slope is -20dB/dec stable, -40dB/dec may be stable or unstable, -60dB/dec may be unstable.
High frequency band: affect the system's anti-interference ability

11. The difference between the characteristics of a nonlinear system and a linear system
1) Whether it satisfies the principle of superposition
2) Whether it is possible to produce self-excited oscillation
3) Whether the stability of the system is related to the initial state

12. The real system has a certain degree of non-linear and time-varying characteristics, but the reason why the linear time-invariant model is often used in theoretical analysis and design
1) Usually the system works in a small range near the equilibrium point
2) Approximate accuracy meets engineering needs
3) The analysis and design methods of the linear system are mature.
4) When the nonlinearity is obvious, the nonlinear method must be used for analysis.

13. What is observability
According to the input signal $u\left(t\right)$ and input signal$y\left(t\right)$ can determine each component in the state vector at the initial moment, and the system is said to be completely observable.

14. What is the separation theorem?
If the system is controllable and observable, the desired closed-loop pole configuration through the feedback gain matrix and the configuration of the observer pole can be performed separately, and they do not affect each other.

15. Talk about the characteristics, background and comparison of modern control theory and classic control
1) Research object
Classical control theory generally studies single-input single-output, linear time-invariant systems.
Modern control theory can study not only single-input single-output systems, but also multiple-input and multiple-output systems. It can analyze not only linear systems, but also nonlinear systems, not only time-invariant systems but also time-varying systems.
2) Mathematical model
Time domain analysis methods of classical control Differential equations, difference equations, frequency domain analysis methods include root locus method, frequency domain method, the mathematical model is the transfer function to express the
modern control theory uses the state space to express the model
3) Application field
classic Control has developed earlier and is widely used.
4) Research content:
Classical control studies dynamic performance, focusing on steady-state quasi-
modern control theory, linear system theory, optimal control, stochastic system theory and optimal estimation, system identification, adaptive control, nonlinearity System theory, robustness analysis and robust control, distributed parameter control, discrete event control, intelligent control.

16. What is the relationship between the control accuracy and the accuracy of the feedback detection device?
The accuracy of the controller and the accuracy of the feedback detection device determine the control accuracy

17. The feedback influence pole is known, and the influence of feedback on the zero point
may increase the zero point. Introduce feedback, open-loop zero or zero point, feedback pole will also become closed-loop zero point, closed-loop zero point will generally affect the dynamic performance of the system (for example, PD control will introduce zero point)

18. What is the Laplace transform of the differential link? Is physics achievable?
s, physics is not realizable, because all systems in nature have limited bandwidth, and the differential link is unlimited bandwidth.

19. What is the meaning of the time constant T of the first-order system? For step signals, the larger the T, the better or the smaller the better?
T represents the time required for the response to reach 63.2% of the final value. For a step signal, the smaller T is, the better

20. What are the stability criteria?
1) Helviz criterion: all Helvíz determinants are greater than 0
2) Linnard-Chipart criterion: all coefficients of the closed-loop characteristic equation are greater than 0, and the odd-order or even-order Helvíz determinants are greater than 0
3) Routh criterion: the number of positive and negative transformations in the first column of the Routh table is the number of closed-loop poles in the right half plane
4) Logarithmic frequency criterion: Z = P-2N (N is greater than the cut-off frequency , The number of times the phase-frequency curve crosses -180 degrees)
5) Nyquist criterion: Z = P-2N (N is the number of times that the phase frequency curve crosses the negative real axis less than -1)
6) In the equation of state, the characteristic root of matrix A All are in the left half plane of s
7) Phase plane method

21. The components of the closed-loop system
1) Given element
2) Comparison element
3) Correction element
4) Amplifying element
5) Actuating element
6) Measuring element

22. How to determine the transfer function of a physical system with unknown internal structure?
Draw a wave diagram through frequency response, and write the transfer function based on the wave diagram

23. If only one input signal is given, how to determine its transfer function.
According to the step response, it is approximated to a first-order or second-order system

24. Can an unstable system be controlled to make the system stable?
Not necessarily. If it is a controllable system, you can configure the poles to make the system stable. If the system is uncontrollable, you cannot configure the unstable poles to make the system stable.

25. How to approximate high-order systems?
1) Select the dominant pole
2) The closed loop gains are equal

26. In the three forms of differential equation, transfer function, and state space equation, what quantities are the natural frequencies of the second-order system given?
$s^2+2\xi {\omega }_{n}s+{\omega }^2=0$ , in the differential equation, the zero-order term is the square of the natural frequency, and the transfer function is${\omega }_n$, Λ 1 λ 2 in the state space $\sqrt{{\lambda }_1{\lambda }_2}$

27. Examples of nonlinear
saturation, relay, hysteresis, gap

28. Initial value theorem and final value theorem
$f(0)={\lim }_{s\to \infty }sF(s)$，$f(\infty )={\lim }_{s\to 0}sF(s)$
$f(0)={\lim }_{z\to \infty }F(z)$，$f(\infty )={\lim }_{z\to 1}(1-{with}^{-1})F(z)$

29.Features of feedback control The
control accuracy is high, and the anti-interference ability is strong. As long as the controlled quantity deviates from the given value, the system will correct the deviation by itself