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Example: Design Lead-Lag Controller
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We all know that control systems are designed for specific tasks. In order to prove suitable performance, it is necessary to change or adjust the design of the control system. This change (adaptation) of the control system is called compensation. The equipment used for this is called a compensator. Standard Compensator The three standard compensator designs (except for gain settings) are lead compensators. delay compensator. Lag lead compensator. Line Compensator A line compensator can be implemented with an electrical network as shown below: Let us now derive the transfer function assuming zero impedance and an infinite impedance of the output load. The output equation is: Laplace transform the above equation, (s) = , (s) = I(s) , take the ratio of (s) and (s) to get the transfer function, = (when simplified) convert the numerator Diving the sum denominator and defining ‘ τ = and α = , we get , , = , so the transfer function is . Now we use jω instead of s to represent the phase equation. (jω) = therefore phase = ∠ (jω) = , since < 1 , the phase of (jω) is positive for all ω 0 . Therefore this network is called a phase lead network. Benefits of the lead compensator Increases system bandwth. It improves the dynamic response of the system. Next we will look at the lag compensator. Delay compensator The delay compensator can be implemented with an electrical network as shown below: Now we derive the transfer function of the delay network: Applying KVL we can get the input and output equations, (t) = i(t) + i(t) + dt , the output equation is (t) = i(t) + dt Using the Laplace transform of the equation, (s) = I(s) + I(s) + , (s) = I(s) + sub Using the ratio of output and input Now if we define τ = and τ = = , the transfer function of the delay compensator becomes (s) = , now for the phase equation we replace s with jω. (jω) = , phase = ∠ (jω) = = = - - , since , the phase of (jω) is negative for all ω 0 . Therefore this network is called a phase delay network. Benefits of Delay Compensator Improved steady-state accuracy. Suppress high frequency noise. A lag-lead compensator A lag-lead network can be implemented with a single gr (see figure below). It's basically a combination of lag and lead networks. Now we will find out the transfer function of the above network as follows: We first apply KVL to get the input and output equations: (t) = , , and the output equation is (t) = i(t) + , , then we need to apply KVL to the above two Laplace transform of the equations: (s) = []I(s) and (s) = []I(s) , taking the ratio of the output and input equations when solving and simplifying, if we get, =, Diving by the counter and denominator, =, we now define =, =, =, and =, we get the transfer function of the LAG-lead compensator as: => 1, Designing the compensator with Bode – Plot: For design purposes, the most Good use of Bode plots. We know that when the open loop gain is changed, the amplitude curve keeps moving up and down without changing the slope of a given curve, and the phase curve remains the same. A common method of designing a compensator using a Bode plot involves the following steps: Plot the magnitude and phase of an uncompensated open-loop system. Check the phase margin and gain margin specifications. If GM and PM specifications are not met, use an appropriate compensator. Determines the transfer function of the open-loop transformation using the selected compensator. Check other requirements to meet specification. Plot a Bode plot using an open-loop transfer transfer function with rate feedback capability. The rate feedback is given by the following equation: (s) = t You can refer to the diagram below: This feedback system offers the possibility to vary three parameters, namely: A, k and . In order to obtain better specified performance, a large number of variables must be introduced into the system. Design becomes more complex. There are two design methods for designing a rate feedback control system. One is based on a single point location and the other is based on a multi-parameter location. A speedometer is one of the rate feedback devices. The other is a rate gyroscope. Rate gyroscopes are often used in aircraft autopilot systems. Speed feedback using a tachometer is very common in position servos.
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Control System – Compensator Design Ultimate Guide !!
In this post you will get complete overview about different types of compensator. Also reader can get clear ea for thier transfer function …
Control Systems – Compensators – Tutorialspoint
The Lag Compensator is an electrical network which produces a sinusoal output having the phase lag when a sinusoal input is applied. The lag compensator …
Getting Started with the Control System Designer – MathWorks
This example shows how to tune compensators for a feedback control system using Control System Designer. Using Control System Designer you can:.
A Review note on Compensator Design for Control Education …
In this paper, the specifications based on time domain analysis such as settling time, rise time, peak time, maximum overshoot etc. are measured from …
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