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By using above standard test signals of control systems, analysis and design of control systems are carried out, defining certain performance measures for the system. Impulse Signal
Introduction: Concept of control system, Classification of control systems - Open loop and closed loop control systems, Differences, Examples of control systems- Effects of feedback, Feedback Characteristics.
- Prof. Shreyas Sundaram
- 1.3 Outline of the Course
- H(s) = : U(s)
- Y (s)
- Bode Plots
- X ! \(j + 1) ; pi
- Solution.
- Modeling and Block Diagram Manipulation
- 6.1 Mathematical Models of Physical Systems
- 6.1.1 Mechanical Systems
- 6.1.2 Electrical Systems
- 6.1.3 Rotational Systems
- H(s) = = : U(s) sn + an 1sn 1 + + a1s + a0
- H(s) = : sn + an 1sn 1 + + a1s + a0
- Performance of Second Order Step Responses
- !2 H(s) = n s2 + 2 !ns + !2
- 8.3 E ects of Poles and Zeros on the Step Re-sponse
- !2 H(s) = n : s2 + 2 !ns + !2 n
- n H(s) = K ; s2 + 2 !ns + !2
- Stability of Linear Time-Invariant Systems
- 1 + + b1s + b0 N(s)
- 9.2 Stability of the Unity Feedback Loop
- R(s) E(s) Y (s) C(s) P(s)
- + P(s)C(s) :
- H(s) = = : sn + an 1sn 1 + + a1s + a0 D(s)
- 9.3.4 Testing Parametric Stability with Routh-Hurwitz
- Properties of Feedback
- + Y (s) C(s) P(s)
- P(s) : P(s) Try(s)
- Y (s)
- Tdy(s) = = 1 : D(s)
- Tdy(s) = = : D(s) 1 + P(s)C(s)
- (1 + P(s)C(s))2 P(s)C(s) 1 + P(s)C(s) 1+P(s)C(s)
- Tracking of Reference Signals
- R(s) E(s) Y (s) C(s) P(s)
- Try(s) = = : R(s) 1 + P(s)C(s)
- Solution.
- (1 + P(s)C(s))sm
- Solution.
- s P(s)C(s)
- C(s) = KP + :
- 12.3 Proportional-Integral-Derivative (PID) Con-trol
- C(s) = KP KI
- 12.4 Implementation Issues
- Root Locus
- Try(s) = = = : 1 + KL(s) D(s) + KN(s) (s)
- 13.1.1 Phase Condition
- Solution.
- 13.2 Rules for Plotting the Positive Root Locus
- 13.2.4 Breakaway Points
- Solution.
- K L(s)
- Solution.
- Margins from Bode Plots
- Stability Margins
- PM 100 :
- Compensator Design Using Bode Plots
- Solution.
- s + p
- s + p
- s s s
- s + p
- = Kc
- 15.3 Lag Compensator Design
- s + p
- Solution.
- Nyquist Plots
- (s + pn)
- X \(s + pi) :
- 16.1 Nyquist Plots
- 16.3 Stability Margins from Nyquist Plots
- Nyquist Plots With Uncertainty and Delay
- Modern Control Theory: State Space Models
- 17.1 State-Space Models
- C |{z} x
- 17.2 Nonlinear State-Space Models and Lineariza-tion
- | {z } a
- Solution.
- 17.4 Obtaining the Poles from the State-Space Model
- Kx(t);
- BK)x:
Department of Electrical and Computer Engineering University of Waterloo
Since control systems appear in a large variety of applications, we will not attempt to discuss each speci c application in this course. Instead, we will deal with the underlying mathematical theory, analysis, and design of control systems. In this sense, it will be more mathematical than other engineering courses, but will be di erent from other m...
The function H(s) is the ratio of the Laplace Transform of the output to the Laplace Transform of the input (when all initial conditions are zero), and it is called the transfer function of the system. Note that this transfer function is independent of the actual values of the inputs and outputs { it tells us how any input gets transformed into the...
Note: The transfer function is the Laplace Transform of the impulse response of the system.
A Bode plot is a plot of the magnitude and phase of a linear system, where the magnitude is plotted on a logarithmic scale, and the phase is plotted on a linear scale. Speci cally, consider the linear system with transfer function H(s) N(s) = D(s). For the moment, assume that all poles and zeros of the transfer function are real (to avoid cumbersom...
i=1 and thus it su ces to consider the phase on a linear scale. Note that we can always draw Bode plots for any transfer function by simply evaluating the magnitude and phase for each value of ! and then plotting these values. However, will want to come up with some quick rules to sketch these plots.
As we can see from the above example, the magnitudes of the two transfer functions do not depend on whether the zero is in RHP or the LHP. However, the phase plots are quite di erent. Based on the above analysis, we see that the phase contribution of a zero in the right half plane is always at least as large (in absolute terms) as the phase contrib...
With the mathematical foundations from the previous chapters in hand, we are now ready to move on to the modeling of control systems.
The rst task of control system design is to obtain an appropriate mathematical model of the plant. In many applications, this can be di cult to do, as ex-perimental data is often noisy, and real-world systems are often quite complex. Thus, we must frequently come up with an approximate model, maintaining a tradeo between complexity and how accurate...
The key equation governing the model of many mechanical systems is Newton's Law: F = ma. In this equation, F represents the vector sum of all the forces acting on a body, m represents the mass of the body, and a represents the acceleration of the body. The forces acting on the body can be generated by an outside entity (as an input to the system), ...
Standard components in electrical systems include resistors, capacitors and inductors, connected together in various ways. The quantities of interest in electrical systems are voltages and currents. Figure 6.1: (a) Components of Electrical Systems. (b) An Electrical System. The main modeling technique for electrical systems is to use Kircho 's Laws...
When the system involves rotation about a point, the system dynamics are governed by a modi ed form of Newton's Law: = J . Here, is the sum of all external torques about the center of mass, J is the moment of inertia of the body, and is the angular position of the body (so that is the angular acceleration). Example: A DC motor consists of an electr...
In practice, many systems are actually nonlinear, and there is a whole set of tools devoted to controlling such systems. One technique is to linearize the system around an operating point, where the nonlinearities are approximated by linear functions. In the rest of the course, we restrict our attention to lin-ear systems, and assume that these lin...
The degree (n) of the denominator polynomial is called the order of the system. As we have already seen, systems of order one and two arise frequently in prac-tice; even when the order of a system is higher than two, one can sometimes approximate the system by a rst or second order system in order to obtain intuition about the system's behavior. It...
We have seen that the step response of a second order system with transfer function
n will have di erent characteristics, depending on the location of the poles (which are a function of the values and !n). We will now introduce some measures of performance for these step responses.
So far, we have been studying second order systems with transfer functions of the form
This transfer function produced a step response y(t), with Laplace Transform
n for some constant K. In this case, the step response is simply scaled by K, but the time characteristics (such as rise time, settling time, peak time and overshoot) of the response are not a ected. We will now consider what happens when we add zeros or additional poles to the system.
Recall from our discussion on step responses that if the transfer function contains poles in the open right half plane, the response will go to in nity. However, if all poles of the transfer function are in the open left half plane, the response will settle down to the DC gain of the transfer function. To describe these characteristics of systems, ...
H(s) = = : sn + an 1sn 1 + + a1s + a0 D(s) Recall that this system is stable if all of the poles are in the OLHP, and these poles are the roots of the polynomial D(s). It is important to note that one should not cancel any common poles and zeros of the transfer func-tion before checking the roots of D(s). Speci cally, suppose that both of ...
Consider the standard feedback structure shown below.
np(s) nc(s) Suppose that we write P(s) = and C(s) = for some polynomials dp(s) dc(s) np(s); dp(s); nc(s); dc(s). The transfer function from r to y is given by H(s)
+ np(s)nc(s) dp(s)dc(s) dp(s)dc(s) + np(s)nc(s) The denominator of the above transfer function is called the characteristic poly-nomial of the closed loop system, and we have the following result. The unity feedback system is stable if and only if all roots of the characteristic polynomial dp(s)dc(s) + np(s)nc(s) are in the OLHP. Note that the abov...
We would like to determine whether all poles of this transfer function are in the OLHP. One way to do this would be to actually nd the poles of the system (by nding the roots of D(s)). However, nding the roots of a high-degree polynomial can be complicated, especially if some of the coe cients are symbols rather than numbers (this will be the case ...
In control system design, we will frequently run across cases where some of the coe cients of the polynomial are parameters for us to design or analyze (such as control gains, or unknown values for system components). We can use the Routh-Hurwitz test to determine ranges for these parameters so that the system will be stable. Example. In the feedba...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
The dynamics of the closed loop system are given by the matrix A BK; speci cally, as discussed in the previous section, the poles of this system are given by the eigenvalues of this matrix. Thus, in order to obtain a stable system, we have to choose K so that all eigenvalues of A BK are stable (i.e., in the OLHP). It turns out that it is possible t...
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Contents. Chapter 1: Introductory Concepts. 1.1 Concepts of Plant, System and Control System. 1.1.1 Examples of Control Systems. 1.1.2 Block Diagram Representation of Control Systems. 1.2 Basic Components of a Control System. 1.3 Classification of Control Systems. 1.3.1 Open-loop and Closed-loop Control Systems.
Download PDF of lecture notes for B.Tech (II-year) course on control system engineering. Learn about open loop and closed loop systems, time and frequency response analysis, state space analysis and more.
Jan 1, 2010 · This book is designed to introduce students to the fundamentals of Control Systems Engineering, which are divided into seven chapters namely Introduction to Control Systems, Laplace Transform...
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What is a Control System? A control system is an interconnection of components forming a system configuration to provide a desired system response. Basic Control System Components Plant (or Process) - The portion of the system to be controlled - Actuator - An actuator is a device that provides the motive power to the process (i.e., a device that
