دانشجو: ناصر علمی غیاثی استاد درس: دکتر توحید خواه پاییز 89

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Presentation transcript:

دانشجو: ناصر علمی غیاثی استاد درس: دکتر توحید خواه پاییز 89 Fast MPC:عنوان سمینار دانشجو: ناصر علمی غیاثی استاد درس: دکتر توحید خواه پاییز 89

فهرست مطالب: مقدمه کاربردها روش های حل ارائه ی چند مثال

مقدمه: تعریف سیستم سریع: سیستمی که برای کنترل آن زمان نمونه برداری باید در حد ثانیه و میلی ثانیه باشد. سیستم پیچیده: سیستمی که تعداد المان های آن و تعاملات آنها زیاد و پیچیده باشد. تعداد متغیرهای حالت و ورودی و خروجی ها زیاد باشند. سیستم غیرخطی: معادلات حاکم بر سیستم غیرخطی بوده و محاسبات بهینه سازی آن پیچیده باشد.

کاربردها: کنترل پایداری خودرو

کاربردها: کنترل احتراق در موتور دیزلی هدایت و ناوبری تصمیم گیری

روش های حل: استفاده از توابع: Laguerre Functions B-Spline Functions Bezier Functions این روش ها بر اساس تقریب عمل می کنند. برای مثال ورودی کنترلی را بر اساس تعداد محدود و اندکی توابع Laguerre تقریب زده می شود. هدف مسئله ی بهینه سازی محاسبه ی ضرایب Laguerre می باشد. این روش ها برای سیستم های پیچیده، با تعداد متغیر حالت زیاد و خطی قابل استفاده است.

روش های حل: تبدیل مسئله ی غیر خطی به تکه ای خطی: تبدیل مسئله ی غیر خطی به خطی متغیر با زمان (LTV) تبدیل مسئله ی غیرخطی به مسئله ی PWA(Piece wise affine) استفاده از روش Active Set برای مسائل PWA روش های سریع و تقریبی interior-point توزیع مسئله ی بهینه سازی بدون تغییر دینامیک سیستم: Control Parameterization Approach (CPA) Multiple shooting real-time iteration …

LPV(Linear Parameter Varying)

LPV(Linear Parameter Varying)

LPV(Linear Parameter Varying)

PWA(Piece wise affine) - the implementation of MPC requires the online solution of a QP at each time step. - Multi parametric quadratic program (mp-QP) H,F,G,W,E can be easily obtained from the plant model.

PWA(Piece wise affine) EGR: exhaust gas recirculation valves VGT: variable geometry turbochargers MAF: mass air flow MAP: intake manifold absolute pressure

Active Set Constraints are active in x0 Numerical and iterative for solve QP problem , offline or Online. for each region, constraints are different and so we have different steps.

Active Set

Active Set

Control Parameterization Approach (CPA) این روش دینامیک سیستم را تغییر نمی دهد. بلکه کنترلر را پارامتری می نماید. the CPA consists basically in the computation of the steady state control u and the definition of a temporal parameterization that structurally meets the constraints. The steady state control u and the corresponding stationary state x can be calculated by solving a simple optimization problem.

Control Parameterization Approach (CPA) the following temporal parameterization can be defined: P: design parameter مسئله تبدیل به مسئله ای برای تعیین P می گردد.لذا متغیرهای مسئله به بردار p تقلیل یافت.

Control Parameterization Approach (CPA) The real time platform used is a 480MHz Autobox-dSPACE system. The routines were developed in C language using the Matlab environment . Sampling period is 50 ms.

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