Fundamentals of Accounting
1. Shannon's sampling theorem? The relationship between sampling frequency and computer hardware The
highest frequency of frequency components contained in a continuous signal is wmax w_{max}wmax, If the sampling frequency w> 2 wmax w>2w_{max}w>2 wmax, Then the continuous signal can be recovered from the sampled signal without distortion, otherwise frequency aliasing will occur. The higher the sampling frequency, the higher the requirements for the computer's operating speed and AD/DA conversion speed.
2. What is the distortion of the sampling signal?
1) Failure to meet the sampling theorem will cause frequency aliasing.
2) Failure to meet the sampling theorem will cause aliasing. The high-frequency components of the signal will be folded into low-frequency components.
3) When the frequency spectrum is infinite bandwidth, no matter how you increase the sampling frequency, there will be frequency. Aliasing
4) When the frequency of a continuous signal is an integer multiple of the sampled signal, hidden oscillation will occur, and this frequency component will disappear in the sampled signal.
Solution: add a pre-filter (anti-aliasing filter) to filter out higher than ws 2 \dfrac{w_s}{2}2ws(Nyquist frequency) frequency components to avoid spectrum aliasing and filter out high-frequency interference.
3. Ideal and undistorted restoration requires 3 conditions:
1) The original signal spectrum is of limited bandwidth
2) It satisfies the sampling theorem
3) It has an ideal low-pass filter to filter the sampled signal
4. Pulse transfer function G (z) G (z)Can G ( z ) be realized?
The denominator order is greater than or equal to the numerator order, physics can be realized
5. Characteristics of frequency characteristics of discrete systems
1) Periodicity
2) Even symmetric amplitude-frequency characteristics
3) Odd symmetrical phase-frequency characteristics
6. The influence of sampling period on frequency characteristics
produces phase delay. For example, the phase lag produced by ZOH is w T 2 \dfrac{wT}{2}2wT
7. Discrete second-order system is judged to be stable.
Necessary and sufficient conditions: ∣ Δ (0) ∣ <1, Δ (1)> 0, Δ (− 1)> 0 |\Delta(0)|<1,\Delta(1 )>0,\Delta(-1)>0∣Δ(0)∣<1,Δ ( 1 )>0,Δ ( - 1 )>0
8. The influence of sampling period on stability
Generally speaking, the smaller the sampling period (closer to the real system), the more stable the system
9. The relationship between steady-state error and sampling period
For a sampling system with a zero-order holder, the steady-state error has nothing to do with the sampling period
10. The relationship between the pole and the dynamic performance
1) The closer to the origin, the faster the convergence
2) The more to the left, the more violent the oscillation
3) Convergence in the unit circle, divergence outside the unit circle
11. Continuous domain-discretization design steps
1) According to the system performance, select the sampling frequency
2) Consider the ZOH phase lag, design the control algorithm transfer function D (s) D (s)D ( s )
3) Choose the appropriate discretization method
4) Verify performance
5) Program to achieveD (z) D(z)D(z)
12. Commonly used discretization methods [Matlab implementation click here]
Under what circumstances can be discrete? Ensure system stability
1) Backward differential
mapping corresponds to one-to-one, frequency is not aliased, stability before and after conversion is the same, steady-state gain remains unchanged, distortion is serious, and conversion accuracy is low
2) Forward difference
mapping one-to-one correspondence, frequency is not aliased, stable before transformation, not necessarily stable after transformation, steady-state gain remains unchanged, and the mapping relationship is severely distorted
3) One-to-
one correspondence between bilinear transformation and pre-corrected bilinear transformation mapping, no frequency aliasing, consistent stability before and after transformation, constant gain in steady state, frequency distortion, the same order of denominator before and after transformation, and the same numerator and denominator order, higher precision
pre-correction can correct a critical frequency characteristic of a continuous and uniform discrete frequency.
4) Zero-pole matching method:
Zero-pole one-to-one mapping, no frequency aliasing, consistent stability before and after conversion, static gain matching, no frequency distortion, good effect, and inconvenient conversion
5) z-transform method (impulse response invariant method)
6) z-transform method with ZOH
13. PID algorithm discrete, the
integral link adopts bilinear transformation, and the differential link adopts backward difference
14. Anti-integral saturation algorithm
1) Integral separation method
Set the error threshold, and no integration will be performed if the threshold is exceeded
2) Limit weakening integration method
Set the control signal threshold, which is greater than the threshold value. If the error decreases, the integration will be accumulated, and the error will not be accumulated if the error is increased. The same is true when the error is less than the threshold.
3) Saturation stop integration method
Set the control signal threshold, and stop integration when the threshold is exceeded
15. The method of PID parameter tuning
1) Expanded critical proportionality method
2) Stable boundary method
3) Expanded step response method
4) Trial method
16. Discrete domain design
1) Root locus method
2) Zero-pole cancellation method
3) w ′ w'w′ Transformation, frequency domain design
17. Controllable and reachable
Controllable: from the initial state to 0.
Reachable: from the initial state to any state. The
sampling system is controllable and reachable. Equivalent, necessary and sufficient conditions: reachable array full rank
18. Observable and reconfigurable
Observable: the initial state
can be determined according to the input. Reconfigurable: the current state can be determined according to the input. The
sampling system is reconfigurable and equivalent. The necessary and sufficient condition: the observable array is full
19. After adding closed-loop feedback, the change of
observability may change from observable to unobservable
20. I/O control mode between CPU and A/D conversion circuit
1) Inquiry mode
2) Interrupt mode
3) DMA mode
21. The role
of the input buffer to buffer, strengthen and gate external signals
22. The role of
the output latch The data or control signal output by the CPU is latched, for example, in the case of time-division multiplexing of the data bus and the address bus, so that the amplifying drive actuator acts on the controlled object
23. I/O electrical conversion part
filtering, level conversion, isolation, power drive, etc.
24. Isn't the sampling period as small as possible?
If the sampling period is too small, the sensitivity of the control algorithm to parameter changes will increase, and the parameters of the control algorithm cannot be accurately expressed, which will cause the characteristics of the control algorithm to change significantly.
25. Selection of sampling period The
system time constant is T d T_dTd, The sampling period is selected as T <T d 10 T<\dfrac{T_d}{10}T<10Td
26. What are the characteristics of machine language, assembly language, and high-level language, and which language has the fastest execution speed?
Execution speed: machine language> assembly language> high-level language.
Machine language is a language that only machines can recognize. There are only 0 and 1 in the program. Programming is difficult and error-prone.
Assembly language is close to machine language and can directly operate on the computer's memory. Can recognize this language.
High-level language is easier for people to write and recognize than assembly language, but it needs to be compiled to run the program.
27. What is the role of the retainer?
Filtering the sampled signal can reproduce the main frequency component and filter out the additional high-frequency component, and restore the digital signal to a continuous signal without distortion
28. Conditions for the stability of discrete systems
All the poles of the closed-loop impulse transfer function are in the unit circle of the z-plane.
29. Which parts of the typical structure of computer and control consist of
hardware + software
Hardware: host, process input and output equipment, human-machine interface equipment, communication equipment
Software: system software, application software, management software
30. Compared with the conventional continuous control system, what are the characteristics of
computer control, flexible design and control, centralized monitoring and operation, comprehensive control, high reliability, and strong anti-interference
31. What are the types of A/D conversion chips?
Counter type, parallel comparison type, double integral type, successive approximation type
32. What transformations must A/D complete to transform a continuous signal into a digital signal? What determines the A/D conversion error mainly?
Sampling, quantization, and coding. A/D conversion rate and conversion accuracy (quantization error)
33. What is the minimum beat system,
also known as the minimum adjustment time system, means that the system has the fastest response speed to typical input signals, and after at least half a sampling period, the steady-state error of the output is zero, so that the output can completely track the input the goal of
34. What is the ringing phenomenon
The output of the digital controller greatly attenuates the oscillation at 1/2 sampling frequency. Due to the low-pass characteristic of the inertial link in the controlled object, this oscillation has almost no effect on the output of the system, but it will increase the wear of the actuator.
35. The problem with the minimum shot?
1) There may be ripples between sampling points.
2) It has poor adaptability to various typical signal input functions.
3) It is sensitive to changes in the model parameters of the controlled object.
36. The minimum beat and ripple-free control must meet the conditions
1) The controlled object has enough integral links
2) The stability of the ripple control and the physical achievable requirements of the controller are met
37. Zero-Order Holder (ZOH) The
zero-order holder is actually the zero-order term obtained by Taylor expansion of the time domain response of an ideal low-pass filter, also known as zero-order extrapolation.
ZOH compared with ideal low-pass filter
1) Ideal filter cut-off frequency wc = ws 2 w_c = \dfrac{w_s}{2}wc=2ws, Signals smaller than the cut-off frequency pass through without distortion, and signals larger than the cut-off frequency cut off sharply at the cut-off frequency. ZOH has an unlimited number of cut-off frequencies wc = nws w_c = nw_swc=nws, The amplitude of the sampled signal varies with www is decreasing.
2) The zero-order keeper is a phase lagging link, the lagging phase isw T 2 \dfrac{wT}{2}2wT
38. Post filter to
reduce the impact of high-frequency noise on the dynamic performance of the system, a low-pass filter can be added behind the retainer