Automation Systems Lecture 7 - Process identiﬁcation Jakub Mozaryn

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Automation Systems

Lecture 7 - Process identification

Jakub Mozaryn

Institute of Automatic Control and Robotics, Department of Mechatronics, WUT

Warszawa, 2016

Jakub Mozaryn Automation Systems

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Controlled process

Controlled proces

Controlled process is a technological process that is under influence of disturbances, where an external control (control) algorithm performs the desired action and enforces desirable behavour of this process.

Mathematical description of the controlled process (simplified SISO - single input single output)

y = f (u, z) (1)

where: y - process variable, u - control variable, z - disturbance.

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Controlled process

G_ob(s) = ym(s)

U(s) = PV (s)

CV (s) (2)

Process variables

Process variables are output variables (y_i;i =, . . . , n) that characterize controlled process.

Process variables characterize the controlled process and their desired course is defined in a control task.

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Controlled process

Gob(s) = ym(s)

U(s) = PV (s)

CV (s) (3)

Input variables

An amount of supplied energy or matter are an input variables xi;i = 1, ..., n of controlled process

To realize technological process there should be provided the relevant streams of matter or streams of energy. The desired course of the process variables depend on these streams and their parameters.

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Controlled process

Gob(s) = ym(s)

U(s) = PV (s)

CV (s) (4)

Disturbances

Disturbances (zi; i = 1, . . . , n) are input signals which adversely affects the course of the process variables.

Disturbances may directly affect the process or distort the streams of energy or streams of matter, eg. in a temperature control in furnace such interference are changes in the calorific value of the fuel.

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Controlled process

Gob(s) = y_m(s)

U(s) = PV (s)

CV (s) (5)

Control variables

Control variables (u_i; i = 1, ..., n) are the input variables generated by the controller.

Actuators, as a result of an influence of the control signals, shape streams of matter or energy according to the control task.

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Controlled process

G_ob(s) = ym(s)

U(s) = PV (s)

CV (s) (6)

Symbols:

u(s) = CV (s) CV - control variable,

ym(s) PV - process variable (from the sensor).

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Selection of elements of control systems

Rysunek:Schematic diagram of the process with actuator (electromagnetic valve) in a) normal model, b) reverse mode

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Classification of controlled processes

Due to the type of equations:

linear, nonlinear.

Due to the behavior in the steady state of step response:

static - having the ability to achieve equilibrium, astatic - not having the ability to achieve equilibrium.

Due to the number of process variables:

one-dimensional, multi-dimensional.

Due to the stability of parameters in time:

time invariant (stationary), nonstationary.

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Controlled process

Step response of the static processes: 1- first order lag element, 2, 3 – higher order lag elements, 4 – oscillatory, 5 - proportional.

Step response of the astatic processes: 1- integral element, 2 - integral element with first order lag, 3 - integral element with first order lag and delay.

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Experimental determination of the time characteristics of controlled process

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Models of the static process

The characteristic features of the step response of the higher order lag elements are fixed time gains T1and T2defined by the tangent to the step response at the point of inflection (as given in a picture).

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Models of the static process

model 1 - first order lag with delay G (s) = ∆ym(s)

∆u(s) = kob

(T_zs + 1)e^−T⁰^s (7) model 2 - Strejc model

G (s) = ∆y_m(s)

∆u(s) = k_ob

(Tzs + 1)ⁿ (8) model 3 - Strejc model with delay G (s) = ∆ym(s)

∆u(s) = kob

(Tzs + 1)ⁿe^−T⁰^s (9)

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First order lag model with delay

Model 1 - Tangent method

T0= T1; Tz = T2 (10)

Model 1 - Secant method

Assumption: The step response of the model in 2 points corresponds with the step response of the process.

P = 0, 5PV → t₁; P = 0, 632PV → t₂ (11) Using the time equation of step response of the first order lag element:

y (t) = ustk(1 − e⁻^T^t), (12) the following equations are obtained:

T₀= t₁− t2ln 2

1 − ln 2 , (13)

Tz = t2− T0= t2− t1

1 − ln 2. (14)

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Higher order lag elements

Model 2 - Strejc model, G (s) = y (s)

u(s) = 1

(Ts + 1)ⁿ (15) n T1/T T2/T T1/T2

1 0 1 0

2 0,282 2,718 0,104 3 0,805 3,695 0,218 4 1,425 4,463 0,319 5 2,100 5,119 0,410 6 2,811 5,699 0,493 Tablica:Parameters of the higher order lag elements

G (s) = y (s)

u(s) = 1

(Ts + 1)⁶ (16)

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Static processes models - example

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Astatic process models - identification

Integral element with first order lag Integral element with first order lag and delay

Gob(s) = 1

T_zs(T₀s + 1) (17) G_ob(s) = 1

Tzse^−T⁰^s (18)

Gob(s) = 1

T_zs(T₁s + 1)e^−T⁰^s (19) G_ob(s) = 1

Tzse^−(T⁰^+T¹^)s (20)

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