Glossary

Glossary: A Acceleration: The change in velocity as a function of time. Accuracy: Measure of the difference between the commanded and the actual position of the motor or a mechanical system. Actuator: A device that causes the process to provide the output; the device that provides the motive power to the process. Amplitude: The size or magnitude of a signal Angle of Departure: The angle at which the locus leaves a complex pole in the s-plane. Asymptote: The path the root locus follows as the parameter becomes very large and approaches infinity. The numbers of asymptotes is equal to the number of poles minus the number of zeros. B Bandwidth: The frequency at which the frequency response has declined 3 db from its low frequency value Block Diagram: Unidirectional operational block that represents the transfer functions of the elements of the system. Bode Plot: defined for an LTI system with transfer function H; refers to two plots: (i) a plot of 20log10 |H(jω)| versus log10 ω on a semilog graph - called the magnitude response or spectrum and (ii) a plot of angle of H(jω) versus log10ω on a semilog graph - called the phase response or spectrum. Also referred to as the frequency response or spectrum of the system H. Break frequency: The frequency at which the asymptotic approximation of the frequency response for a pole (or zero) changes slope. Breakaway point: The point on the real axis where the locus departs from the real axis of the s-plane. C Characteristic equation: The relation formed by equating to zero the denominator of a transfer function. Closed-loop feedback control system: A system that uses a measurement of the output and compares it with the desired output. Closed-loop frequency response: The frequency response of the closed loop transfer function T(jω) Compensation: The alteration of adjustment of a control system in order to provide a suitable performance. Complementary Root Locus: The complementary root locus for a negative feedback system with open loop transfer function L(s) = k n(s)/d(s) is a plot in the s-plane of the roots of the closed loop characteristic equation d(s) + k n(s) = 0 as the scalar constant k is varied from 0 to minus infinity. Controllable system: A system with unconstrained control input u that transfers any initial state X(o) to any other state X(t) Corner Frequency: For first order time constants, the "corner frequency" is the frequency where the amplitude ratio starts to turn and the phase lag equals 45 degrees. Critical damping: A critically damped system responses to a change in the desired velocity or position with the minimum possible time and little or no overshoot. Critically damped is preferred over an under- or over-damped system. Critically Damped Poles: refers to identical real poles that are stable (i.e. lie in the open left half plane). Such poles have a damping ratio zeta of unity and are associated with decaying exponentials in the time domain. D Damped oscillations: time. An oscillation in which the amplitude decreases with Damping ratio: A measure of damping. A dimensionless number for the secondorder characteristic equation. Decibel (dB): The unit of the logarithmic gain. Differential Amplifier: One whose output is proportional to the difference between two inputs. Digital control system: A control system using digital signals and a digital computer to a process. Discrete I/O: Senses or sends either "on or off" signals to the field. For example a discrete input would sense the position of a switch. A discrete output would turn on a pump or light. Dominant roots: The roots of the characteristics equation that cause the dominant transient response of the system. E Error Signal: The difference between a desired quantity and the actual quantity. F Feedback signal: A signal that is transferred from the output back to the input for use in a closed loop system. Feedback System - refers to a sytem, which uses feedback measurements to enhance the properties of a physical system called the plant. Feedforward compensation: A corrective action to improve system performance such as accuracy and response time. Feedforward precompensates for known errors due to the motor, drive, or lead characteristics. Filter: A transfer function used to modify the frequency or time response of a control system. Frequency: Measured in hertz (cycles per second), rate of repetition of changes Frequency response: The steady-state response of a system to a sinusoidal input signal. G Gain: The ratio of the system output to the input. Gain Margin: The difference in the logarithms of the amplitude ratios at the frequency where the combined phase angle is 180 degrees lag is the GAIN MARGIN H Hertz (Hz): Cycles per second, unit of frequency. Hurwitz Polynomial: a polynomial with its roots in the open left half plane. I I/O (Input/Output): The reception and transmission of information between control devices. ISO: International Standards Organization L Laplace transform: A transformation of a function f (t) from the time domain to the complex frequency domain yielding F(s) Linear Time Invariant (LTI) System: A dynamical systems, which are linear and time-invariant. Locus: A path of trajectory that is traced out as a parameter is changed Logarithmic magnitude: The logarithm of the magnitude of the transfer function 20log10 |G| Logarithmic plot: See Bode Plot M m: Symbol for meter and milli- (thousandth). Mason loop Rule: A rule that enables the user to obtain a transfer function by tracing paths or loops within a system Mathematical Models: mathematics Descriptions of the behavior of a system using Minimum phase: All the zeros of a transfer function lie in the left-hand side of the s-plane N Natural frequency: The frequency of natural oscillation that would occur for two complex poles if the damping were equal to zero. Negative feedback: The output signal is feedback so that it subtracts from the input signal Nichols chart: A chart displaying the curves for the relationship between the open loop and closed-loop frequency response. Nonminimum phase: Transfer functions with zeros in the right-hand s-plane Number of separate loci: Equal to the number of poles of the transfer function assuming that the number of poles is greater than the number of zeros of the transfer function. Nyquist stability Criterion: A feedback system is stable if, and only if, the contour in the G(s) plane does not encircle the (-1,0) point when the number of poles of G(s) in the right-hand s-plane is zero. If G(s) has P poles in the righthand plane, then the number of the encirclements of the (-1,0) point must be equal to P for a stable system O On-Off Control: A simple control system that is either on or off. Open-loop control system: A system that utilizes a device to control the process without using feedback. Thus the output has no effect upon the signal entering the process Open Loop Poles: refers to poles (finite or at infinity) of the open loop transfer function. Open Loop Zeros: refers to zeros (finite or at infinity) of the open loop transfer function. Oscillation: Variation, usually with time, of the magnitude of a quantity with respect to a specified reference when the magnitude is alternately greater and smaller than the reference. Overshoot: The amount the system output response proceeds beyond the desired response. Output: Information leaving a device Overdamped Poles - refers to distinct real poles, which are stable (i.e. lie in the open left half plane). Such poles have a damping ratio zeta, which lies, in the interval (1, infinity) and are associated with decaying exponentials in the time domain P Parameter design: A method of selecting one or two parameters using the root locus method Peak time: The time for a system to respond to a step input and rise to a peak response. Phase-lag Network: A network that provides a negative phase angle and the significant attenuation over the frequency range of interest. Phase-lead Network: A network that provides a positive phase angle over the frequency range of interest. Thus phase-lead can be used to cause a system to have an adequate phase margin Phase Margin: Amount of phase lag, which can be introduced into a feedback loop before the closed loop system goes unstable. Plant: Physical system to be controlled; system whose properties we want to alter via feedback. Polar plot: A plot of the real versus the imaginary part of G(jω). Pole: value of s in the complex plane at which a real-rational transfer function approaches infinity; refers to natural frequencies of a system. Also called mode or natural mode. Positive feedback: The output signal is feedback so that it adds to the input signal. Process: The device, plant, or system under control R Ramp Input: A steadily rising signal. Range: The maximum and minimum allowable full-scale signal (input or output). Reference Command: An externally applied signal, which represents a command; usually represents the desired output Resonant Frequency: The frequency, ωr, at which the maximum value of the frequency response of complex pair of poles is attained. Rise Time: refers to the time required for the output of a system to reach 90% of the final output value in response to a specific input. The rise time depends on the applied signal and on the dynamical properties of the system Robust control: A system that exhibits the desired performance in the presence of significant plant uncertainty. Root locus: The locus or the path of the roots traced out on the s-plane as a parameter is changed. Root locus procedure: The method for determining the locus of the roots of the characteristic equation 1+KP(s) = 0 as K varies from 0 to infinity. Routh-Hurwitz criterion: A criterion for determining the stability of the system by examining the characteristic equation of the transfer function. The criterion states that the number of roots of the characteristic equation with positive real parts is equal to the number of changes of sign of the coefficient in the first column of the Routh array. Routh Table: A table formed from the coefficients of a polynomial. The table is used to determine the number of right half plane roots of the polynomial. It is also useful for determining the location of any roots, which are symmetric with r espect to the origin. S Series Compensation: A compensator, which is in series with the plant. Other forms of compensation include Parallel Compensations and Feedforward Compensation. Settling Time: The time required for the system output to settle within a certain percentage of the input amplitude. Signal-flow graph: A diagram that consists of nodes connected by several directed branches and that is a graphical representation of a set of linear relations. Simulation: A model of a system that is used to investigate the behavior of a system by utilizing actual input signal. Stability: A performance measure of a system. A system is stable if all the poles of the transfer function have negative real parts. Stable System: A dynamic systems with a bounded system response to a bounded input. State of a system: A set of numbers such that the knowledge of these numbers and the input function will, with the equations describing the dynamics, provide the future state of the system. State variables: The set of variables that describe the system. State differential equation: The differential equation for the state vector: X  Ax  Bu Steady-state error: The error when the time period is large and the transient response has decayed, leaving the continuous response Step Response: The response of a system to a step function. Unless otherwise specified, a unit step function input under zero initial conditions is implied. System: An interconnection of elements and devices for a desired purpose. . T Test input signal: An input signal used as a standard test of a system’s ability to respond adequately. Time delay: A pure time delay, T, so that events occurring at time t at one point in the system occur at another point in the system at a later time, (t+T) Time domain: The mathematical domain that incorporates the time response and the description of a system in terms of time, t Time varying system: A system for which one or more parameters may vary with time. Transfer function in the frequency domain: The ratio of the output to the input signal where the input is a sinusoidal. It is expressed as G(jω). Transient: A short surge of current or voltage, often occurring before steadystate conditions have become established. Transient response: The response of a system as function of time. Transition matrix  (t ) : The matrix exponential function that describes the unforced response of the system. Type number: The type number, N, of the poles of the transfer function G(s), at the origin. G(s) is the forward path transfer function U Undamped Poles: A set of complex conjugate poles on the imaginary axis that has a zero damping ratio zeta and are associated with undamped sinusoidal oscillations in the time domain. Underdamped Poles: A set of complex conjugate poles, which are stable. Such poles have a damping ratio zeta, which lies, in the interval (0, 1) and are associated with exponentially decaying sinusoids in the time domain. Unstable System: The systems, which possess at least one pole in the open right half plane or a double pole at the origin or complex conjugate double poles on the imaginary axis. The first is associated with a rising exponential or a rising exponential sinusoid. The latter two are associated with ramp-like signals in the time domain. V Velocity error constant, Kv: The constant evaluated as limit {sG(s)} for a type one system. The steady state error for a ramp input for a type one system is equal to A/ Kv. Z Zero: Input frequencies, which are absorbed by a system. Zero Input Response: Response of a system with the input set to zero; response to an initial condition with no input. Zero State Response: Response of a system with the state set to zero; response to an input with zero initial condition.