文档介绍：Chapter 6
Parameter Identification From Step Response
Li Shaoyuan
E-mail: ******@sjtu.
Outline
Parameter Identification from Step Response
Theoretical Step-Response Expressions
Classical methods for open loop step test
Log Method
Two Points Method
Area Method
Least Squares Methods
Classical Closed-Loop step test
Least squares method for system under PID control
Problem formulation
Recursive Solution
Transfer function modeling
Basic Requirement
Basic Requirement
Obtain simple process model from a transient response experiment.
inject step input at the process
measure response
Requirement:
the process must be stable.
Amplitude of step signal must be set a pripori
sufficiently large so response is easily visible above noise level
as small as possible
not to disturb the process more than necessary
keep the dynamics linear.
Theoretical Step-Response Expressions
First-order-plus-time-delay
Parameters:
K, τ, L.
Second-order-plus-time-delay
Parameters:
K, τ1, τ2, L.
Single zero, two poles, plus time delay
Parameters:
K, τ1, ξ, τ2, L.
Classical Methods For Open Loop Step Test
Log Method
First order process when times greater than the time delay
Thus, a plot of the transformation of the step-response data against time t should be a straight line with a slope of -1 / τ, and an intercept on the ordinate of L / τ. Also, this straight line will meet the t-axis at the point t = L. We may therefore obtain estimates of these parameters graphically.
estimate of the steady-state gain
Time Constant τ and Time Delay L:
Two Points Method
y(∞)%

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time(t)
T/3+L
T/2+L
+L
+L
T+L
+L
2T+L
t1 and t2, the time when response with value % and %
Process model and step response
Area Method
the average residence time Tar puted form the area of A0
Measure pute area A1 under step up to the time Tar
Than T and L can be estimated as
Least Square Method For Open Loop Step Test