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Performance Assessment of PID Controllers based on MV and LQG Criteria

Mousavi, Hossein | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45983 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Nobakhti, Amin
  7. Abstract:
  8. In this thesis, a new method for the design and Control Performance Assessment (CPA) of the Rrestricted-Structure (R-S) PID controllers family (P, I, PI, PD …) is proposed. The proposed method is capable of a systematic analysis of the tradeoff between the structural complexity of the controller and its performance.During the past two decades, control performance assessment has attracted much at- tention from academic and the industrial researchers. One of the most recent tools is the RS-CPA, proposed by Grimble in which restricted structure controllers such as the PID are assessed against optimal LQG measures. When one is able to impose a specific structure onto the controller, such as a PID, then the ‘choice’ of the control structure becomes a new additional design parameter. For a SISO system, the number of choices might be limited to a few (e.g. PI, PID, PD). However, when the plant is multivariable, the number of alter- native combinatorial choices will rapidly increase in size. It is then a non-trivial exercise to select an appropriate structure. Under these circumstances, the structure of the controller becomes an optimization parameter itself and the design problem becomes the simultane- ous optimization of performance and minimization of the structure. Typically the balance of the design may be influences by a weighting factor which determines the ratio of the contribution of the performance and the structure costs. In this thesis, first, a suitable framework is proposed for application of the LQG CPA to multivariable decentralized PID controllers. The problem is augmented with an addi- tional term which forces sparsity on the structure of the decentralized PID controller. The desired ‘richness’ of the structure is controlled via a weighting parameter which increased or decreases the cost of each additional structural elements (i.e. P,I, and D) terms. The result is a decentralized multivariable controller of the PID family, in which the structure of each loop controller is not fixed or determined a priory, but is instead optimized in such a way that the desired LQG PI index, is delivered with the smallest controller structure. For larger multivariable systems, this will translate into a substantially reduced set of controller parameters Numerical simulation results indicate the effectiveness of the proposed algorithm in terms of design and CPA, both in SISO and MIMO settings
  9. Keywords:
  10. Performance Evaluation ; Decentralized Controller ; Proportional-Integral-Derivative (PID)Controller ; Linear Quadratic Gaussian (LQG)Controller ; Restricted Structure Controller ; Basis Pursuit Regularisation (BPR)Algorithm

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