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    The candidate must have sound electrical engineering and controls knowledge as the role will include control system definition, standards, design, specification…. Aerospace control system engineer. Or MEng with a technical engineering background in electrical, mechanical, software or systems engineering. The expression resulting from this exercise is useful in various control system analysis and design procedures. Each block in the diagram must represent a linear system expressed in the form of a transfer function.

    Transfer functions are introduced in Chapter 3. Knowledge of the details of transfer functions is not required to perform block diagram algebra.

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    Lower case characters identify the signals in this system. The blocks in the diagram represent linear system components. Each block can represent dynamic behavior with any degree of complexity as long as the requirement of linearity is satisfied. The fundamental rule of block diagram algebra states that the output of a block equals the block input multiplied by the block transfer function. Applying this rule twice results in Eq. In words, Eq. Block diagram algebra obeys the usual rules of algebra. Multiplication and addition are commutative, so the parentheses in Eq.

    This also means that the positions of the G c and G p blocks in Fig. The error signal e is the output of a summing junction subtracting the sensor measurement from the reference input r. The sensor measurement is the system output y multiplied by the sensor transfer function H. This relationship appears in Eq. Equation 1. This form of system model is suitable for use in numerous control system analysis and design tasks. Using the relation of Eq. Remember, these manipulations are only valid when the components of the block diagram are all linear.

    One of the first steps in the control system development process is the definition of a suitable set of system performance specifications. Performance specifications guide the design process and provide the means for determining when a controller design is satisfactory. Controller performance specifications can be stated in both the time domain and in the frequency domain. Time domain specifications usually relate to performance in response to a step change in the reference input.

    An example of such a step input is instantaneously changing the reference input from 0 to 1. Time domain specifications include, but are not limited to, the following parameters [1]:. Examples of these parameters appear in Fig. This figure shows the response of a hypothetical plant plus controller to a step input command with an amplitude of one.

    The time axis zero location is the instant of application of the step input. The step response in Fig. Sometimes the step response has no overshoot at all. When no overshoot occurs, the t p parameter becomes meaningless and M p is zero. Tracking error is the error in the output that remains after the input function has been applied for a long time and all transients have died out. It is common to specify the steady-state controller tracking error characteristics in response to different commanded input functions such as steps, ramps, and parabolas.

    In addition to the time domain specifications discussed above, performance specifications can be specified in the frequency domain. The controller reference input is usually a low frequency signal, while noise in the sensor measurement used by the controller often contains high frequency components. It is normally desirable for the control system to suppress the high frequency components related to sensor noise while responding to changes in the reference input. Performance specifications capturing these low and high frequency requirements would look similar to these:.

    Definition

    In other words, the frequency domain performance requirements given above say that the system response to expected changes in the reference input must be acceptable while simultaneously attenuating the effects of noise in the sensor measurement. Looked at in this way, the closed loop system exhibits the characteristics of a lowpass filter. Stability is a critical issue throughout the control system design process.

    A stable controller produces appropriate responses to changes in the reference input. If the system stops responding properly to changes in the reference input and does something else instead, it has become unstable. The initial response to the step input overshoots the commanded value by a large amount. The response to that overshoot is an even larger overshoot in the other direction. This pattern continues, with increasing output amplitude over time. In a real system, an unstable oscillation like this grows in amplitude until some nonlinearity such as actuator saturation or a system breakdown!

    System instability is a risk when using feedback control.


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    Avoiding instability is an important part of the control system design process. In addition to achieving a bare minimum degree of stability, a control system must possess a degree of robustness. A robust controller can tolerate limited changes to the parameters of the plant and its operating environment while continuing to provide satisfactory, stable performance. For example, an automotive cruise control must maintain the desired vehicle speed by adjusting the throttle position in response to changes in road grade an environmental change. The cruise control must also perform properly whether or not the vehicle is pulling a trailer a change in system parameters.

    Determining the allowable ranges of system and environmental parameter changes is part of the controller specification and design process. To demonstrate robustness, the designer must evaluate controller stability under worst-case combinations of expected plant and environment parameter variations. For each combination of parameter values, a robust controller must satisfy all of its performance requirements. When working with linear models of plants and controllers it is possible to precisely determine whether a particular plant and controller form a stable system.

    Chapter 3 describes how to determine linear system stability. If no mathematical model for the plant exists, stability can only be evaluated by testing the plant and controller under a variety of operating conditions. Chapter 2 covers techniques for developing stable control systems without the use of a plant model. Chapter 9 describes methods for performing thorough control system testing. Testing is an integral part of the control system design process.

    Many of the design methods in this book rely on the use of a linear plant model. Creating a linear model always involves approximation and simplification of the true plant behavior. The implementation of a controller using an embedded processor introduces nonlinear effects such as quantization. As a result, both the plant and the controller contain nonlinear effects that are not accounted for in a linear control system design.

    The ideal way to demonstrate correct operation of the nonlinear plant and controller over the full range of system behavior is by performing thorough testing with an actual plant. This type of system-level testing normally occurs late in the product development process when prototype hardware becomes available. Problems found at this stage of the development cycle tend to be very expensive to fix. Because of this, it is highly desirable to perform thorough testing at a much earlier stage of the development cycle.

    Early testing enables discovery and repair of problems when they are relatively easy and inexpensive to fix. However, testing the controller early in the product development process may not be easy if a prototype plant does not exist on which to perform tests. System simulation provides a solution to this problem [2]. A simulation containing detailed models of the plant and controller is extremely valuable for performing early-stage control system testing.

    This simulation should include all relevant nonlinear effects present in the actual plant and controller implementations. While the simulation model of the plant must necessarily be a simplified approximation of the actual system, it should be a much more authentic representation than the linear plant model used in the controller design. When using a simulation in a product development process, it is imperative to perform thorough simulation verification and validation. The verification step is relevant for any software development process, and simply shows that the software performs as its designers intended.

    In simulation work, verification can occur in the early stages of a product development project. It is possible and common to perform verification for a simulation of a system that does not yet exist. This consists of making sure that the models used in the simulation are correctly implemented and produce the expected results. Verification allows the construction and application of a simulation in the earliest phases of a product development project. Validation is a demonstration that the simulation models the embedded system and the real world operational environment with acceptable accuracy.

    A standard approach for validation is to use the results of system operational tests for comparison against simulation results. This involves running the simulation in a scenario that is identical to a test that was performed by the actual system in a real world environment. The results of the two tests are compared and the differences are analyzed to determine if they represent significant deviations between the simulation and the actual system.

    A drawback of this approach to validation is that it cannot happen until a complete system prototype is available. Even when a prototype does not exist, it may be possible to perform validation at an earlier project phase at the component and subsystem level. You can perform tests on those system elements in a laboratory environment and duplicate the tests with the simulation. Comparing the results of the two tests provides confidence in the validity of the component or subsystem model.

    The use of system simulation is common in the control engineering world.

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    If you are unfamiliar with the tools and techniques of simulation, see reference [2] for an introduction to this topic. The classical control system analysis and design methods discussed in Chapter 4 were originally developed and have been taught for years as techniques that rely on hand-drawn sketches. While this approach leads to a level of design intuition in the student, it takes significant time and practice to develop the necessary skills. Since this book intends to enable the reader to rapidly apply a variety of control system design techniques, automated approaches will be emphasized rather than manual methods.

    Several software packages are commercially available that perform control system analysis and design functions as well as complete nonlinear system simulation. Some examples are listed below. These tools provide efficient, numerically robust algorithms to solve a variety of control system engineering problems. The MATLAB environment also provides powerful graphics capabilities for displaying the results of control system analysis and simulation procedures.

    If you are a student using the software in conjunction with courses at a degree-granting institution, you are entitled to purchase the MATLAB Student Version and Control System Toolbox at a greatly reduced price. Feedback control systems measure attributes of the system being controlled and use that information to determine the control actuator signal. Feedback control provides superior performance compared to open loop control when environmental or system parameters change.