第五章
PID控制回路
杨根科
上海交通大学自动化系
2007年3月
计算机控制系统框图
闭环控制结构
一个PID控制系统
Composition control system for a stirred-tank blending process
Notation:
w1, w2 and w are mass flow rates
x1, x2 and x are mass fractions of component A
Assumptions:
w1 is constant
x2 = constant = 1 (stream 2 is pure A)
Perfect mixing in the tank
Control Objective:
Keep x at a desired value (or "set point") xsp, despite variations in x1(t). Flow rate w2 can be adjusted for this purpose.
Terminology:
Controlled variable (or "output variable"): x
Manipulated variable (or "input variable"): w2
Disturbance variable (or "load variable"): x1
Design Question. What value of is required to have
Overall balance 流量平衡:
Component A balance 组份平衡:
(The overbars denote nominal steady-state design values.)
At the design conditions, . Substitute Eq. 1-2, and , then solve Eq. 1-2 for :
Control Question. Suppose that the处inlet concentration x1 changes with time. How can we ensure that x remains at or near the set point xSP
As a specific example, if x1 减 and w2 增, then x > xSP.
Some Possible Control Strategies:
Method 1. Measure x and adjust w2.
Intuitively, if x is too high, we should reduce w2;
Proportional feedback control law,
where Kc is called the controller gain.
w2(t) and x(t) denote variables that change with time t.
The change in the flow rate, is proportional to the deviation from the set point, xSP – x(t).
Method 2. Measure x1 and adjust w2.
Thus, if x1 is greater than , we would decrease w2 so that
One approach: Consider Eq. (1-3) and replace and with x1(t) and w2(t) to get a control law:
一个PID控制系统
Control Block Diagram
一个PID控制系统
Block Diagram for Entire Blending Process Composition Control System