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## Connection between PID, Pole placement and LQR

- \$\begingroup\$ I just stumbled across this, but am having the same problem. \$\endgroup\$ – Sam Spade Nov 21, 2017 at 14:41
- 1 \$\begingroup\$ I think the following conference paper provides a solution, ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=760858 \$\endgroup\$ – Hazem Dec 14, 2017 at 17:29

- \$\begingroup\$ -1: I think there are some points in your answer that are not right. I don't think that LQR & PPR are the same regulators. LQR gives some guaranteed stability margins whereas PPR does not provide them. They both use state feedback but they are not the same. I also do not think that a system needs to be observable in order to place the poles arbitrarily but it needs to be controllable. The last paragraph is also wrong as this article provides a method how to use the LQR gains for a PID design ( waset.org/publications/9999411/… ). \$\endgroup\$ – MrYouMath Dec 14, 2017 at 16:44
- \$\begingroup\$ Someone should fix this answer as the general structure was enlightening to me, so I would like to see the details ironed out. After reading this, I come to the conclusion that LQR and PPR are similar in that they use state observers (unlike PID), and that PID and PPR are similar in that they think in frequency domain in terms of a transfer function (as opposed to LQR). Is this a fair way to compare them? \$\endgroup\$ – samlaf Apr 2, 2020 at 14:30

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## Comparison of LQR and Pole Placement Design Controllers for Controlling the Inverted Pendulum

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## IMAGES

## VIDEO

## COMMENTS

Linear Quadratic Regulator is an optimal technique of pole placement method which defines the optimal pole location based on a definite cost function.

Linear Quadratic Regulator (LQR) is the optimal theory of pole placement method. LQR algorithm defines the optimal pole location based on two cost function.

LQR or PPR regulators are both state-space regulators, which use the states of the system in order to bring the poles of the closed loop

Two types of regulators are studied, the State-Regulator using Pole Placement, and the Linear-Quadratic regulator (LQR). The LQR is obtained by resolving

pendulum in the vertical position. After linearization, we have: V.

Linear Quadratic Regulator is an optimal technique of pole placement method which defines the optimal pole location based on a definite cost function. The

pole/placement LQR technique. Fig 4. Plant with state feedback. V. POLE PLACEMENT DESIGN. Pole placement method is a controller design method in which the

some conclusions are given in Section V. ... feedback gain matrix of pole placement.

To stabilizes and control the position of rolling Ball on the beam, Pole Placement Technique and Linear Quadratic Regulator (LQR) Controller has been applied on

امهو نيتيمزراوخ. Simulated Annealing (SA) optimization. و. Ant Colony (AC) optimization. ترهظا . ةقيرط قوفت جئاتنلا. LQR. رطيسم ميمصتل state

Or, even if we can change the pole locations. • Where do we put the poles? — Linear Quadratic Regulator. — Symmetric Root Locus. • How well does this approach