CDS Central

FAQ (Frequently Asked Questions)

Category: CDS 101/110 Fall 2003

Identifiers: FN H0 H1 H2 H3 H4 H5 H6 H7 H8 L0.0 L1.1 L1.2 L10.1 L2.1 L2.2 L3.1 L3.2 L4.1 L4.2 L5.1 L5.2 L6.2 L8.1 L9.1 L9.2

Questions

Answers

In Example #2 (cruise control), was "b" damping and "k" the gain?
Submitted by: lars
Submitted on: September 29, 2003
Identifier: L1.1
Yes, on both counts.
In this example the first equation represents a model of the dynamics of the vehicle. The constant "b" is a damping factor on the speed of the vehicle (with units of "force per velocity").
The second equation represents the control algorithm for the cruise control. The constant "k" represents a gain factor on the error in the velocity (the desired velocity minus the actual velocity). This determines how "aggressive" the cruise controller will be.
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What is "control gain", and how is it used?
Submitted by: lars
Submitted on: September 29, 2003
Identifier: L1.1
The term "control gain" refers to the constant multiplier that appears in any controller description. For example, in the cruise control example from lecture ("Example #2"), the equation that described the controller was
u_engine = k*(v_des-v).
In this controller, the control gain is the constant k. In terms of how it is used, in this case there is a computer in the car that takes the desired and current velocities and computes the torque that is applied to the engine (u_engine) according to the above equation.
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What is actuation?
Submitted by: lars
Submitted on: September 29, 2003
Identifier: L1.1
"Actuation" refers to the means of effecting control on a given system. For example, the throttle (or, alternatively, the engine) is considered an "actuator" for the car in the cruise control example (equivalently, the actuation).
In most of our examples, we will use the variable "u" as representing the control input to a system. For example, the throttle position (or the engine torque) is the control input in the cruise control example. The control input affects the system being controlled by means of its actuation.
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Can you say more about feedforward control?
Submitted by: lars
Submitted on: September 29, 2003
Identifier: L1.1
Feedforward control is a mechanism of control in which the control is affected by a priori known or predicted disturbances. The term "feedforward" is used since it describes the forward (left-to-right) flow of signals in a standard block diagram.
Feedforward control has its benefits and drawbacks. Here is a nice article on feedback versus feedforward control that includes discussion of a simple example.
Feedforward control can be used in conjunction with feedback control to improve the performance of the system. However, with both types of control their effectiveness relies on use of a sufficiently good model of the system being controlled.
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In the cruise control example, what does 'des' stand for in v_des?
Submitted by: mreiser
Submitted on: September 29, 2003
Identifier: L1.1
'des' is short for desired. So in the cruise control example v_des is the desired velocity for the vehicle. In a typical vehicle this would be the desired velocity that the driver would set for the cruise controller. In the case of Bob, the autonomous vehicle, yet another control system would actually set this desired velocity for the cruise control system.
On slide # 11, where the cruise control example is shown, there is also a block diagram (upper right corner). In this diagram the 'reference' input represents v_des. Calling the desired setpoint a 'reference input' is rather common terminology.
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Please define "dynamics" of a system.
Submitted by: lars
Submitted on: September 29, 2003
Identifier: L1.1
There are two important uses of the word dynamics. One is in reference to the actual physical (biological, financial, etc) phenomenon, and the way it evolves in time, and the second is in reference to a MODEL of that process (i.e. a differential equation).
Regarding the former, we use the term informally to include any kind of characteristics that evolve in time (e.g. the speed of a car, what gear its in, etc.). In this usage, the "dynamics" is the process of interest, the thing which is to be MODELED.
The latter usage will refer, almost exclusively, to a differential equation (equivalently, a transfer function, if the Laplace transform is utilized). This will typically be something of the form $dx/dt = f(x)$. The variable $x$ is the state of the system, and we refer to the differential equation as (a model of) the dynamics.
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What about robustness to variations in the sensing or feedback itself?
Submitted by: lars
Submitted on: September 29, 2003
Identifier: L1.1
It is definitely true that variation in sensing and feeback mechanisms (say a miscalibrated sensor) will deteriorate the performance (and perhaps stability) of a control system. The extent to which this falls outside the scope of the original comment regarding robustness to variation in dynamics depends on the model (i.e. to what extent sensors are assumed to be perfect).
Assuming that feedback mechanisms are perfectly modeled at the analysis or design stage can cause potentially serious detriment, since the controller is designed to operate on perfect measurements. On the other hand, the feedback framework (think block diagrams and arrows) naturally lends itself to including sensor properties in the dynamics. Instead of a setup like:
System Output --> Controller --> System Input
The model could be:
System Output --> Sensor Mechanism --> Controller --> System Input
Imperfections in getting the actual system output to the controller are a serious problem in practical control design, and various tools (some of which we will discuss in this course) exist to combat it.
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Robustness to uncertainty, this is to use feedback to lower the uncertainty, right?
Submitted by: mreiser
Submitted on: September 29, 2003
Identifier: L1.1
This is not exactly right. In general, we are unable to lower the uncertainty associated with the system we wish to control, that is precisely why we must use feedback. Robustness and uncertainty are terms that get used constantly when describing control systems and they occasionally mean different things. For example, in the amplifier circuit example discussed in class, the system we wish to control is uncertain (because the electronic components have significant variations among them). So we employ feedback (all the connections from the output of each amplifier back to its input) to ensure the performance we want.
Here is a definition of Robustness from a textbook [Slotine and Li, Applied Nonlinear Control]: "Robustness is the degree to which a system is insensitive to effects that are not considered in the design." In the circuit example we have not worried about the variations in the components, and yet through feedback we are robust to these details. This makes life easier for the Control Engineer, in many cases a well-designed control system will be robust to many nitty-gritty details one may not wish to model.
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How useful is the recommended text in the bookstore? Is it worth $100?
Submitted by: murray
Submitted on: September 29, 2003
Identifier: L1.1
If you are going to "major" in control (eg, take more than just CDS 110ab), then it would probably make sense to buy a good undergraduate textbook. However, everything you need for CDS 101/110a will be made available online.
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What is UTRC and what is their affiliation with Caltech and this class?
Submitted by: murray
Submitted on: September 29, 2003
Identifier: L1.1
UTRC is the United Technologies Research Center, in Hartford, CT. UTRC is the research arm for the United Technologies Corporation (UTC), which is better know for its operating units -- Pratt & Whitney aircraft engines, Otis elevators, Carrier air conditioners, and Sikorsky helicopters (and a few others). They have a number of collaborations with Caltech and Richard Murray spent two years on sabbatical there, hence the connection.
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Can you switch between CDS 101 and 110?
Submitted by: murray
Submitted on: September 29, 2003
Identifier: L1.1
Yes. It's easiest to switch from CDS 110 to 101, since you will be doing all of the CDS 101 homework for CDS 110. If you switch the other way, you will lose credit on the problems that you don't turn in (worth approximately 50% of each homework).
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Are the classes videotaped? How can I access the videos?
Submitted by: murray
Submitted on: September 29, 2003
Identifier: L1.1
CDS 101 and 110 will be videotaped and the videos made available in VHS format for checkout by the students. We will put the videos in the boxes outside of 102 Steele. Look in Box G for the CDS 101/110 tapes. It may take us a few days to get this set up, but eventually the tapes for each lecture should be available within a day or two of the lecture (we have to transfer them to VHS).
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What does 'audit' mean (on the sign up sheet)?
Submitted by: murray
Submitted on: September 29, 2003
Identifier: L1.1
Faculty, staff, and students are welcome to "audit" CDS 101 or 110, which means that you sit in the course but don't actually take it for a grade. You are welcome to do the homework (a good way to learn!), but we ask that if you are not taking the course that you grade your own homework sets (solutions will be posted on the web), since it takes the TAs time and effort to grade and we can only do this for students that are registered for the course.
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Are control system designed to work under specific conditions (i.e. a Flyball Governor is designed to maintain a particular speed)? How flexible can they be?
Submitted by: mreiser
Submitted on: September 29, 2003
Identifier: L1.1
Typically a control system is designed for a specific purpose, i.e. to control the rotation rate of a steam engine, control the velocity of a car, control the temperature of a room, etc. However, we try to design systems that operate under a broad set of conditions, as in the cruise control example, we design the control system (by choosing the gain, k) to ensure good performance of the system in many condition (full/empty tank, flat/hilly terrain, dry/wet weather, etc.).
Typically control systems are designed with at least one reference input. This input, e.g. the desired speed of the cruise controller or the desired temperature for a thermostat, determines the particular output we would like our system to achieve. In the case of the Flyball Governor the control input is not obvious, so it might seem that this controller can only maintain a particular speed. The Flyball Governor can be thought of as a mechanical circuit, with the linkage mechanism connecting the weights (Flyballs) to the valve, acting as a mechanical amplifier. The linkage mechanism can be adjusted, thus the reference speed for the steam engine can be set to any value. Incidently, here is a provocative little write-up about the Flyball Governor from Kevin Kelly's interesting book "Out of Control" which is available online.
As far as how flexible a control system can be... In general control system are designed to meet certain performance specifications, i.e. a particular thermostat might be guaranteed to regulate temperatures in the range of 40-110 degree farenheit, for normal uses this seems perfectly 'flexible' though it might not be wise to install this controller on the space shuttle or in an research station in Antarctica. Although you can still find some mechanical control systems around, these days many commercial control systems are designed using very flexible electronic hardware. Microcontrollers are the little devices providing much of the computation for the control systems in cars, microwave ovens, soda machines, etc. Microcontrollers are popular because they usually combine several input and output channels with a programmable processor in a small, low-cost package. A Control Engineer might use the same exact microprocessor to implement a control system for many typical engineering control systems (I won't give any more examples, this is your job on HW 1), the only thing that needs to change is the software on the device. Recently, there are many research efforts to streamline the software development for these so-called "embedded" control systems so that the details of the control system need not be too strongly tied to the particular microcontroller.
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Why are the two main principles of control presented in L1.1 called "principles"? Why are there only two of them?
Submitted by: lars
Submitted on: October 9, 2003
Identifier: L1.1
[Continuation of question]: Was anything eliminated when making this choice? Later the same principles are called "principles of feedback". Why?
[Response]: The principles presented (Robustness to Uncertainty through Feedback and Design of Dynamics through Feedback, slide 10 of L1.1) are called principles because they are an essential characteristic of the effects of proper control design.
Listing two doesn't imply that there are only two essential characteristics of feedback control (alternatively "feedback", or "control"; these each usually refer to and mean feedback control), but these are perhaps the most central to a general understanding of why feedback control is important.
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What is the difference between a system's error and a system's uncertainty?
Submitted by: mreiser
Submitted on: October 9, 2003
Identifier: L1.1
The 'error' is what we typically call the quantity that is fed back into the controller, the difference between the desired system set-point and the current one. This would be the difference between the commanded and current speed in the cruise control system. When we refer to a system's 'uncertainty' we typically mean effects that have not been accounted for in our model of the system. These are things like changes in mass of a vehicle due to tread wear or fuel consumption, etc (for the cruise control example). Another example of system uncertainty is the electronic component inconsistencies in the example discussed in lecture 1.
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You seem to use uncertainty and disturbance interchangeably...
Submitted by: waydo
Submitted on: October 9, 2003
Identifier: L1.1
...are they the same? If not, what are the differences?
The word "uncertainty" refers very broadly to anything we don't know about the system, and can be expressed with questions like: Did we get the right values for parameters such as stiffness? Are the inputs from the actuators exactly what we desire? Are there inputs not under our control (such as wind loads or temperature variations, etc.)?
The word "disturbance" is a little more specific and usually refers to signals entering the system that are not under our control such as sensor and actuator noise and external forces, so a disturbance is really a type of uncertainty.
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Please elaborate on stability and performance.
Submitted by: demetri
Submitted on: October 11, 2003
Identifier: L1.1
These two issues form the fundamental basis of control engineering, and often define the fundamental tradeoff decision that designers must make.
Loosely speaking, stability is the property of the system converging to its commanded point. There are various technical notions of stability which will be discussed later in the course, but a central idea to grasp is that this describes long-term or steady-state behavior.
On the other hand, performance is essentially a transient issue: how fast and with how much "wobble" do we get where we want to go? High-performance controllers will be "more aggressive" in seeking their equilibrium points. There should be an intuitive tradeoff between "aggressiveness" and stability. It is difficult to make a controller which is both very fast and also very stable.
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Sensing,computing, and actuation: which are central and which are peripheral?
Submitted by: demetri
Submitted on: October 11, 2003
Identifier: L1.1
First, the "official" answer: all three are central. In principle, one should be able to identify sensing, computing, and actuating elements in anything we would meaningfully call a control system (cf HW1).
The practical answer to this question is largely hardware or system dependent. For example, in the steam engine governor, you would have to take a fairly abstract view of "sensing" and "computing" to identify these elements. Many mechanical feedback mechanisms will pose similar problems, such as the gyroscopic stabilization of spinning bodies (think of a top).
Similarly, in more exotic application areas, such as network congestion control, it would probably be difficult to separate computation from actuation concretely; the same device which computes the control law also implements it. Although, abstractly speaking, it does two different things, it would certainly be hard to point to some fundamental physical separation between these phenomena.
Thus, we emphasize the original answer: abstractly speaking, they are all essential. Sometimes, nature or engineering will conspire to embed one within the other, but it is much more useful for us, as designers, to think of them as three separate phenomena.
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