Page : 1 EE406 Control Systems Lecture 20 : Further Control Theory
UCSI University Faculty of Engineering Kuala Lumpur, Malaysia Department of Mechatronics
Lecture 18
The Farewell Lecture :
Further Control Theory
Mohd Sulhi bin Azman Lecturer
Department of Mechatronics UCSI University [email protected]
1 August 2011
Contents
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So far…
1. Control engineering:
– Modeling d
• differential equation, transfer function, state space
– Performance analysis
• time response
– Stability analysis
• pz-map, Routh-Hurwitz
Deterministic System
• A deterministic system is a system in which no randomness is involved in the development of future states of the system.
• A deterministic model will thus always produce the same output from a given starting condition or initial state.
• If the initial state were known exactly, then the future state of such a system could be predicted. However, in practice, knowledge about the future state is limited by the precision with which the initial state can be
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Stochastic System
• Also known as random or probabilistic system. The word stochastic means random.
• A stochastic system is where the inputs and possibly system parameters may have components which vary randomly with time.
• This randomness may be due to the nature – for example, a basic input signal may have been contaminated with an unwanted noise signal.
• Therefore, a stochastic system is usually described by a probabilistic function and their statistical properties i.e. their expected mean value.
Stochastic Control System
• Stochastic control deals with control design with uncertainty in the model.
• In typical stochastic control problems, it is assumed that there exist random noise and disturbances in the model and the controller, and the control design must take into account these random deviations.
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Stochastic Control : Air Traffic Control
Note : FMS = Flight Management System
Robust Control
• Robust control is a branch of control theory that explicitly deals with uncertaintyin its approach to controller design.
• Robust control methods seek to bound the uncertainty rather than express it in the form of a distribution. Given a bound on the uncertainty, the control can deliver results that meet the control system requirements in all cases.
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Optimal Control
• Basically, an optimal control is the process of
determining control and state trajectories for a dynamic system over a period of time to minimise a performance index, J.
• A performance index is the system performance.
• It is an extension of the calculus of variations for dynamic systems with one independent variable, usually time, in which control (input) variables are determined to maximize (or minimize) some measure of the
performance (output) of a system while satisfying specified constraints.
Optimal Control
• The formulation of an optimal control problem
requires the following criteria:
1. a mathematical model of the system to be controlled,
2. a specification of the performance index,
3. a specification of all boundary conditions on states, and constraints to be satisfied by states and
controls,
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Optimal Control
• Consider a car traveling on a
straight line through a hilly road.
• The question is, how should the driver
press the accelerator pedal in order to
minimize
the total traveling time?
• Can you identify the criteria for optimal control
of the car?
Optimal Control
• The required criteria:
– Variables to be controlled :
• the way the driver press the accelerator and shifts the gear
– Optimal criteria (performance index):
• minimization of the total traveling time
– Constraints:
• fuel, speed limits, road surface etc.
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Optimal Control
• The answer:
– find the way to drive the car so as to minimize its fuel consumption, given that it must complete a given course in a time not exceeding some amount.
– another control problem is to minimize the total monetary cost of completing the trip, given assumed monetary prices for time and fuel.
• There are two approaches to optimal control:
– via calculus of variation – via dynamic programming
Optimal Control
• The basis equation of optimal control system is
to minimize the performance index. The
following equation illustrates the process
Lagrangian (running cost between the initial
and final time) Cost function
at terminal (final) time Performance
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Adaptive Control
• Adaptive control involves modifying the control law used by a controller to cope with the fact that the
parameters of the system being controlled are slowly time-varying or uncertain.
• In another word, the adaptive control system changes according to changes in the environment and plant.
• That is, the system adapts itself so as to maintain satisfactory control, which is usually judged by some performance index.
Adaptive Control
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Adaptive Control
• Let us see how can we apply
an adaptive control system.
Consider an aircraft flying.
• As an aircraft flies, its mass will slowly
decrease as a result of fuel consumption;
therefore we need a control law that adapts
itself to such changing conditions.
Nonlinear System
• Many system exhibits nonlinearities – frictions etc.
• Now, non-linearity of a system does not necessarily mean that all the system elements or units need be considered as nonlinear.
• A “separable” system is one in which the nonlinear part can be described:
y=f(x) G(jω)
Nonlinear
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Nonlinear Control
• Nonlinear control is the area of control
engineering specifically involved with systems
that are nonlinear, time-variant, or both.
Intelligent Control
• Intelligent control uses various artificial intelligent (AI) computing approaches to control a dynamic system.
• It is a process that drives an intelligent machine to attain its goal automatically.
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Intelligent Control
• Typical structure of
intelligent
controller.
• Source : Zi-Xing Cai.
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Intelligent Control : Solar Water Heater
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Sophistication in Control
Open Loop Control
Feedback Control
Optimal Control
Stochastic Control
Adaptive & Robust Control
Learning Control
Intelligent Control
Next Step
• Textbook reference : None.
• There is no homework for this lecture. But I
hope that you have truly enjoyed learning
control systems with me. You can come and
consult me should you wish to pursue
postgraduate studies in control engineering.
