This blog post is based on the analysis of automatic control principle exercises (Hu Shousong second edition), answers classic exercises, summarizes the problem-solving rules, and is convenient for students to review. This article belongs to the exercises of automatic control principle. It is driven by exercises and does not only understand the theory. For those who don’t know how to solve the problem, because the author is also reviewing the postgraduate entrance examination and is also a fresh graduate, there will inevitably be some mistakes in the summary. If you find it, please remind it in the comment area, hope to make progress together, and successfully land on the postgraduate entrance examination!
- Topic: Explain the following nouns or simply answer the following questions.
a. Automatic control; b. Automatic control system; c. Principle of feedback control; d. Classification of automatic control system; e. Basic requirements of automatic control system.
Solution:
a. Automatic control: refers to the use of additional equipment or devices (control devices or controllers) to make machines, equipment or production processes (collectively referred to as controlled objects) work in a certain state or The parameter (controlled quantity) automatically runs according to a predetermined rule.
b. Automatic control system: The controlled object and the control device are connected in a certain way to form an organic whole, which is the automatic control system.
c. The basic principle of feedback control : In the feedback control system, the control effect exerted by the control device on the controlled object is the feedback information taken from the controlled quantity, which is used to continuously correct the deviation between the controlled quantity and the input quantity. So as to achieve the task of controlling the controlled object.
d. Classification of automatic control systems:
① According to the control method, it is divided into: open loop control, feedback control, and compound control;
② According to the component type, it is divided into: mechanical system, electrical system, electromechanical system, hydraulic system, pneumatic system, biological system;
③ According to system functions, it is divided into: temperature control system, pressure control system, position control system;
④ According to system performance, it is divided into: linear system and nonlinear system, continuous system and discrete system, steady system and time-varying system, deterministic system and Uncertainty system;
⑤ Divided into constant value control system, follow-up system and program control system according to the law of input change.
e. The basic requirements of the automatic control system: stability, rapidity and accuracy; among them: stability is a prerequisite to ensure the normal operation of the control system, and the stability of the linear automatic control system is determined by the system structure and parameters, and is related to the outside world. The factor has nothing to do.
2. Title: The following figure is a schematic diagram of the principle of the electric furnace stability control system. Try to analyze the working process of the system to keep the electric furnace temperature constant, point out the controlled object, the controlled quantity and the role of each component of the system, and draw the system block diagram.
Test site analysis: Draw system block diagrams and clarify the composition of the system through analysis of working principles.
Solution:
a. The general principle description.
The electric furnace uses resistance wire to heat, and it is required to keep the furnace temperature constant. It is known from the schematic diagram that a thermocouple is used to measure the furnace temperature and convert it into a voltage signal, and the measured voltage signal is fed back to the input terminal and connected with the given voltage signal in reverse polarity to realize negative feedback. The difference between the two is called the deviation voltage, which drives the DC servo motor after voltage amplification and power amplification. The motor drives the movable contact of the voltage regulating transformer through the reducer to change the power supply voltage of the resistance wire, thereby regulating the furnace temperature.
b. A concrete description of the principle.
When the furnace temperature is low, measure the voltage uuu is less than the given voltageu 0 u_0u0, The deviation voltage of the comparison between the two is Δ u = u 0 − u \Delta{u}=u_0-uΔu=u0−u； YuuΔ u \ Delta {u}[Delta] U is positive, the shift motor "n" turn the regulator movable contact, resistance wire supply voltage increases, the current increased, temperature rise, until the furnace temperature was raised to a predetermined value. At this time,u = u 0, Δ u = 0 u=u_0, \Delta{u}=0u=u0，Δu=0 , the motor stops rotating and the furnace temperature remains constant.
When the furnace temperature is high,Δ u \Delta{u}Δ u is negative. After amplifying, the motor turns "reversely", and the movable contact of the voltage regulator moves down to reduce the power supply voltage until the furnace temperature is equal to the given value.
c. The role of each component.
The controlled object of the system: electric furnace; controlled quantity: electric furnace temperature; actuator: servo motor, reducer, speed governor; detection element: thermocouple.
d. Draw a block diagram of the control system.
- Topic: The following formulas are differential equations describing the system, where c (t) c(t)c ( t ) is the output,r (t) r(t)r ( t ) is the input quantity, try to determine which are linear invariant or time-varying systems, and which are non-linear systems.
Test site analysis: classification of automatic control systems.
Systems that can be described by linear differential equations or differential equations are called linear systems; if the coefficients of differential equations or differential equations are all constants, they are called linear time-varying systems; otherwise, they are called linear time-varying systems.
A system described by a nonlinear equation is called a nonlinear system. The characteristics of nonlinear equations: coefficients are related to variables, and the equations contain high power or product terms of variables and their derivatives.
Solution:
a.
c (t) = 5 + r 2 (t) + td 2 r (t) dt 2; (non-linear time-varying system) c(t)=5+r^2(t)+t\frac {d^2r(t)}{dt^2}; (non-linear time-varying system)c(t)=5+r2(t)+tdt2d2 r(t); ( Non- line of the time varying system system )
. B
D. 3 C (T) dt. 3 +. 3 D 2 C (T) dt 2 +. 6 DC (T) dt +. 8 C (T) = R & lt (T); ( Linear time-invariant system) \frac{d^3c(t)}{dt^3}+3\frac{d^2c(t)}{dt^2}+6\frac{dc(t)}{dt}+ 8c(t)=r(t); (linear time-invariable system)dt3d3c(t)+3dt2d2 c(t)+6dtdc(t)+8c(t)=R & lt ( T ) ; ( wire of a given constant based system )
C.
TDC (T) dt + C (T) = R & lt (T) +. 3 DR (T) dt; (varying systems) t \ frac {dc ( t)}{dt}+c(t)=r(t)+3\frac{dr(t)}{dt}; (linear time-varying system)tdtdc(t)+c(t)=r(t)+3dtdr(t); ( Lines of time varying based system )
D.
C (T) = R & lt (T) T [omega] + COS . 5; (nonlinear time-varying systems) c (t) = r (+5; (non-linear time-varying system)c(t)=r(t)cosωt+5 ; ( non- line of the time varying system system )
E.
C (T) =. 3 R & lt (T) +. 6 DR (T) dt + 5 ∫ - ∞ TR ([tau]) D [tau]; (Linear System) (T ips : Derivation on both sides of the equation) c(t)=3r(t)+6\frac{dr(t)}{dt}+5\int_{-\infty}^{t} r(\tau) d\tau; (Linear Time-invariant System) (Tips: Derivative on both sides of the equation)c(t)=3r(t)+6dtdr(t)+5∫−∞tR & lt ( [tau] ) D [tau] ; ( lines of constant often based system ) ( T I P S:Fang Cheng two sides seek guide )
F.
C (T) 2 = R & lt (T); (nonlinear invariant systems) c (t) = r ^nonlinear invariant systems)c(t)=r2 (T);(non-lineofa givenconstantbasedsystem)
G.
C (T) = {0, T <. 6; R & lt (T), T ≥. 6. ; (Linear delay system) c(t)= \begin{cases} 0,&t＜6;\\r(t),&t≥6. \end{cases}; (Linear delay system)c(t)={ 0，r(t)，t＜6;t≥6。; ( Line of delay delayed based system )