Analog Control• All variables in the system are analog representations of another variable.• VT is an analog of T 11
Control System Objectives1. System stability2. Steady-state regulation3. Transient regulation.
Control System Objectives Unstable (un-damped) Response Output Under-damped-response Critical-damped-response Over-damped-response TimeTransient Stability
Control System Objectives Unstable Response Disturbance Output Steady State Error +/- 5% Time Stable ResponseSteady State Stability
Evaluation Criteria1. System must be stable2. Best Response Parameters 1. Fast response 2. Minimum overshot 3. Minimum steady state error3. Minimum Integral Absolute Error4. Maximum quarter amplitude damping
Response Parameters First Overshot Second Overshot Desired Value Output0.9 Steady State Error +/- 5% Period of Oscillation0.1 Time Rise Time
Integral Absolute ErrorError Time IAE E dt
Quarter Amplitude Damping A1 = First Overshot A2 = Second OvershotOutput Damping Ratio = A2/A1 < (1/4) Time
Controller Tuning Adjust controller parameter to get the best system response Steady State ErrorOutput Time
Controller Implementation AnalogAnalog Control Unit DigitalDigital A/D Control D/A Unit
Data RepresentationDigital Representation Analog Representation
Data ConversionsADC (Analog-to-digital converter) DAC (Digital-to-Analog converter)
Data Units• It is essential to use a well-defined set of units of measurement• Two system of units: – The metric system – The English system• In process control, a particular set of metric units is used called the International System (SI)
International System of UnitsQuantity Unit SymbolLength Meter mMass Kilogram kgTime Second s BASEElectric Current Ampere ATemperature Kelvin KAmount of substance Mole molLuminous intensity Candela cdPlane Angle Radian rad SUPPLEMENTARYSolid angle Steradian sr
Process Control Definitions• Control: Force parameters in the environment to have specific values.• Sensor: Convert process output signal to measurable control signal.• Actuator: Convert control signal to process input signal.• Controller: Responsible on evaluating the error, taking the control decision and producing the control signal.
Process Control Definitions• Error:• Difference between the measured value of the variable and the desired one.• Transfer Function• Relationship between the input and output for the block
Process Control Definitions• Transfer Function• Relationship between the input and output for the block, consists of two parts: static and dynamic – Static: Output depends only on input values – Dynamic: Output depends on input and on previous system status
Process Control Definitions Accuracy• Maximum overall error to be expected from a device• Accuracy is usually expressed as: – Measured value • EX (± 0.3 ma) – Percentage of the instrument full-scale (FS) reading • EX (Full Scale 20 ma and accuracy ± 1% ± 0.01*20 ma) – Percentage of instrument span • EX (Span 4 to 20 ma and accuracy ± 2% ± 0.02*(20-4)ma) – Percentage of the actual reading • EX (Read value is 15 ma and accuracy ± 0.5% ± 0.005*15 ma)
Process Control Definitions Sensitivity• Measure of the change in output of an instrument for a change in input• High sensitivity is desirable in an instrument: a large change in output for a small change in input• Ex: A temperature transducer outputs 10 mV per degree Celsius; sensitivity = 10 mV/ºC
Process Control Definitions Hysteresis and Reproducibility• An instrument will not have the same output value for a given input in many trials• This is reproducibility of the device• This variation is random and unpredictable• Hysteresis: Different readings results for a specific input, depending on whether the input value is approached from higher or lower values.
Process Control DefinitionsHysteresis and Reproducibility
Process Control Definitions Resolution• Minimum measurable value of the input variable.• Can be changed only by redesign.• Analog systems: smallest measurable change in the analog output signal of the measurement device.• Digital systems: change in dynamic variable represented by a 1-bit change in the binary word output.
Process Control Definitions Linearity• In sensor and signal conditioning, output is represented in some functional relationship to the input• This relationship must be unique: for each value of the input variable there exists one unique value of the output variable.• A linear relationship between input and output is highly desirable.
Process Control Definitions Sensor Time Response• A process-control loop element specifies how the output is related to the input if the input is constant• An element also has a time dependence that specifies how the output changes in time when the input is changing in time• This dynamic transfer function is called the time response.
Process Control Definitions Sensor Time Responseb(t) = bi+(bf – bi)[1 – e-t/] First Order Response
Process Control Definitions Sensor Time ResponseSecond Order Response• a: output damping constant• fn: natural frequency of the oscillation
Process Control Definitions Significance and Statistics• Significant figures: – Do not attach more significance to a variable value than the instrument can support.• Statistics: – Arithmetic mean and – Standard deviation