Chpt 28 Basic Closed-Loop Control Flashcards
how are control systems often described as
in terms of block diagrams
what is the system in the diagram known as
the plant
what is the control input
the parameter that we change to affect the plant
in the case of DC motor this will be the duty cycle drive of voltage to the motor
what is the output response
the magnitude of the control input
what is the output response
the parameter that we are interested in monitoring and controlling
for DC motor this will be the speed of the motor
what is the step response
the response of the system to an instantaneous change in the command or control input
what is an overdamped response
a response that rises slowly to the new value and always approaches from the direction of the new value of the system output prior to time t=0
what is an underdamped response
a response that exhibits a faster rise time but overshoots the target value and exhibits a decaying oscillation before settling
what is a rise time
the time taken for the value to reach the target value even if it overshoots
what is an overshoot
the amplitude the response goes above the target value before decreasing to go towards the target value again
what is the settling time
the time taken for the response to settle to a stable value
what is a critically damped response
a response that walks the fine line between over and under damped
it exhibits a quick rise time with no overshoot of the final target value
in practise it is difficult and often unnecessary to achieve true critical damping
what is open loop control
you map the response of a system to the control variable and then use that mapping to produce the desired output during operation
what is feedback
the operation of feedback is where the system gives information about the current state of the system
what is bang bang control
the control effort is either fully on or fully off and no attempt to made to modulate an intermediate value of control effort
what is important for bang bang control
the response of the system to the system to the control effort must be relatively slow compared to the rate at which the control effort can be switched on or off
where is bang bang control commonly used
in thermal control systems such as refrigerators baking ovens and heating/cooling systems in buildings
what is chatter in a bang bang system and how can it be overcome
chatter is the rapid turning of the actuator (eg a furnace) on and off when the measured parameter is close to the set point and moves slightly above and below it
to overcome the chattering effect two threshold values are set
the system is turned on till the measurement has reached the upper threshold where it will turn off the actuator and wont be switched on till it reaches the lower threshold
what is the gap between the two threshold setpoints known as
the deadband
what are the two conditions that must be met to consider Bang Bang control
first the system requirement is to allow for the variation in the output response are inherent in on-off control
second being that the combination of the dynamics of the system and the ‘strength’ of the actuator be such that the peak-to-peak variation in the controlled parameter can be limited enough to meet the requirements of the system
what is the simplified equation for control effort a linear closed loop control
Control effort = (Where we want to be - where we are) x scaling factor
what is error
the difference between ‘where we want to be’ and ‘where we are’
what is the scaling factor also known
gain
what is proportional gain
Kp
when the gain is applied directly to the error yielding an effort that is proportional to the error
how can the trapezoidal rule used in control systems
for the integral gain
Current Integral error = change in time x [(error at last step + current error)/2]
how to condense a history of error into a single number to be used for control
Control effort = (Error x Proportional Gain) + (Integral gain x sum of errors)
what is the scaling factor with the summation of errors known as
Ki
integral gain
what is the type of control with a proportional term and an integral term known as
PI control
how does PI control work
proportional only control generated enough control effort to force the duty cycle to its maximum ( often referred to the Saturation of the actuator) by the time the proportional control effort starts to drop off ( after about 20 ms) the integral term has had time to accumulate an integrated error and starts to contribute significantly
the result is the slow rise of the motor speed to the desired set point
what is the ability to overcome external disturbances
disturbance rejection
what is integrator windup
a large accumulated error that caused a large command resulting in overshoot of the target speed
what is the solution to integrator windup
integrator antiwindup
the easiest way to do this would be to monitor the commanded control effort, once it reaches 100% stop integrating the error as the system is already doing everything that it can do to reach the target
the same should be done for 0% duty cycle for the same logic
what would adding a term that looked at the rate of change of the error and use it to reduce or increase the control effort
Control effort = Proportional Gain(Error + (Integral gain x sum of error)+ (derivative gain x dError/dT))
what does adding the derivative control do to the system
adds stability to a system, the added stability compensates for the destabilising effect of the integral control
what is the potential drawback of the derivative term
it may accentuate any noise present in the feedback signal
what needs to be done to implement derivative control
need to keep track of what the error was the last time we updated the control effort so that we can develop a term that is the rate of change of error
what is tuning
the process of selecting the proper gains to create a successful control system
what does adding a proportional term do to the rise time
decreases
what does adding a proportional term do to the overshoot
increases
what does adding a proportional term do to the settling time
No change
what does adding a proportional term do to the Steady state error
Decreases
what does adding a integral term do to the Rise time
Decreases
what does adding a integral term do to the Overshoot
Increases
what does adding a integral term do to the Settling time
Increases
what does adding a integral term do to the steady state error
Eliminates
what does adding a derivative term do to the rise time
No Change
what does adding a derivative term do to the overshoot
Decreases
what does adding a derivative term do to the settling time
Decreases
what does adding a derivative term do to the steady state error
No change
what does increasing the proportional term do to the Rise time
Decreases
what does increasing the proportional term do to the overshoot
Increases
what does increasing the proportional term do to the Settling time
Increases
what does increasing the proportional term do to the Steady state error
Decreases
what does increasing the integral term do to the rise time
Decreases
what does increasing the integral term do to the overshoot
Increases
what does increasing the integral term do to the settling time
Decreases then Increases
what does increasing the integral term do to the Steady state error
Eliminates
what does increasing the derivative term do to the rise time
Increases
what does increasing the derivative term do to the overshoot
Decreases
what does increasing the derivative term do to the settling time
Decreases
what does increasing the derivative term do to the Steady state error
No Change
in Ziegler Nichols tuning what does ‘d’ represent
pseudo delay
in Ziegler Nichols tuning what does ‘T’ represent
the process time constant and is arrived at by drawing a line tangent to the steepest part of the transition curve and extending the line upwards and downwards
T is the time difference between where the tangent intersects the original steady state plant output value and where the tangent intersects the final plant output value
in Ziegler Nichols tuning what does ‘K’ represent
the value K is the measure of how much the plant output changed for a given command change
what is the process gain given by Gp
Gp = K/change in control effort
what is the Proportional gain given by in Ziegler Nichols open loop tuning
Kp = 1.2(T/d.Gp)
what is the Integral gain given by in Ziegler Nichols open loop tuning
Ki = 0.5/d
what is the Derivative gain given by in Ziegler Nichols open loop tuning
Kd = 0.5 . d
