Process Characteristics （过程动态特性分析） Lei Xie Institute of Industrial Control, Zhejiang University, Hangzhou, P. R. China

Contents Importance of Process Characteristics (过程对象特性的重要性) Introduction of Final Control Elements (执行机构介绍) Types of Processes (过程特性分类) Obtaining Characteristics from Process Dynamics (过程特性机理建模法) Obtaining Characteristics from Process Data (过程特性测试建模法) Summary

Heat Exchanger Temperature Control System The extended controlled process (广义对象) is anything except the controller.

Importance of Process Characteristics Every process has different characteristics Not easy to change the controlled process Very easy to change the controller tuning What we can do is to adapt the controller to the process A good controller is the controller best adapted to the process characteristics

Pneumatic Control Valves (气动调节阀) 功能：根据阀头气压的大小，通过阀杆改变阀体中阀芯的位置，进而调节流经阀体的流体流量。

Types of Processes Self-regulating processes (or stable processes, 自衡过程/稳定对象) (1) Single-Capacitance Processes (2) Multi-Capacitance Processes Non-self-regulating processes (or unstable processes,非自衡过程) Ex.: some level processes and some reactors

A Self-regulating Process The controlled process is stable. Why ?

A Non-self-regulating Process The controlled process is unstable. Why ?

A Self-regulating Liquid Level Process The process is self-regulating. Why ?

Approaches to Obtain Process Characteristics Based on Process Dynamics (机理建模) Describe process characteristics with some mathematical equations based on the chemical and/or physical mechanism of a controlled process. Based on Process Data (测试建模) To obtain process characteristics, manually change the input of a controlled process and record the input and output data, then find an appropriate model based on process data.

Modeling Example #1 Material balance equation： Relationship between flow and level： Problem Discussion: How to build the controlled process with SimuLink? (\ProcessModel\ LevelProcess01.mdl)

Modeling Example #2 For the level controlled process, h2 is selected as its controlled variable, and Qi is the manipulated variable, Qd is the main disturbance variable. The rates of outlet flow are assumed to satisfy the following equations: Please obtain the process characteristics by dynamic equations, and build the corresponding Matlab/SimuLink model.

Modeling Example #2 Material balance equation： Relationship between flow and level： Simulation ex.: \ProcessModel\ LevelProcess02.mdl State equation and linearization ?

Single-Capacitance Processes Ex.1

Single-Capacitance Processes Ex.2

Single-Capacitance Processes Ex.3

Terms that Describe the Process Characteristics Process Gain (K) Ratio of the change in output (or responding variable) to the change in input (or forcing function). Process Time Constant (T) Process Dead Time (τ)

Process Gain Calculation Ex.1

Process Gain Calculation Ex.2

Process Gain Calculation Ex.3

Notes to Process Gain Process gain describes the sensitivity of the output variable to a change in input variable. Process gain includes three parts: Sign, Numerical value and Units. Process gain relates only steady-state values, so the gain is a steady-state characteristic of the process.

Process Time Constant (T ) Definition The process time constant for a single-capacitance process is defined as the amount of time counted from the moment the variable starts to respond to reach 63.2% of its total change.

Process Dead Time (τ) Definition the finite amount of time between the change in input variable and when the output variable starts to respond.

Notes to Parameters K, T, τ These numerical values describe the basic characteristics of a real process, which K describes the steady-state characteristic, and T, τ are related to the dynamics of the process. These numerical values depend on the physical parameters of the process as well as its operating conditions. In most cases, they vary with operating conditions, or most processes are nonlinear. The ratio, τ/ T, has significant adverse effects on the controllability of control systems.

Mathematical Description of Single-Capacitance Processes The transfer function for a first-order-plus-dead-time (FOPDT) process is given by

Multi-capacitance Processes Ex.2

Mathematical Description of Multi-Capacitance Processes High-Order Model: Second-order-plus-dead-time Model First-order-plus-dead-time Model

Characteristics of Real Processes Most controlled processes are self-regulating except some liquid level processes; Processes have some amount of dead time; The step responses of controlled processes are often monotonous and slow; Most processes are nonlinear, so the numerical values of model parameters vary with operating conditions.

Parameters Describing Process Characteristics Process Gain (K) Ratio of the change in output (or responding variable) to the change in input (or forcing function). Process Time Constant (T) Process Dead Time (τ)

Obtaining Process Characteristics from Process Data Obtain the necessary process data by step response testing; (1) Set the controller to manual mode; (2) Make a step change in the controller output; (3) Record the process variable. Obtain parameters K, T, τ from process testing data.

The Step Response Curve for a Heat Exchanger

Obtain the Dynamic Terms from the Step Response Curve

Obtain Process Gain from the Step Response Curve If the span of the temperature transmitter is 100 to 300 ℃, then the change in transmitter output is 4%. Therefore, the total process gain is

Summary Defined the types of processes: self-regulating and non-self-regulating processes, single- and multi-capacitance processes ; Discussed the modeling from process dynamics; Discussed process characteristic parameters K, T,τ, and their obtaining methods from process data.

Problem 2-1 For the level controlled process, h2 is selected as its controlled variable, and Qin is the main input of the process. Suppose the sectional area of two tanks are A1 and A2. The rates of outlet flow are assumed to satisfy the following equations: Please obtain the process characteristics by dynamic equations (the ODE equations).

Problem 2-2 Material balance equation： Relationship between flow and level： Please determine the equation that the steady-state operating point (稳态工作点) needs to satisfy. Obtain the process transfer functions around the operating point. Note that