動態系統之強健適應控制器設計

Abstract

對於某一類之耦合線性非時變多輸入多輸出系統，本文根據不同系統的相對階數發展系統化的方法以調整P/PI/PID控制增益。 藉由線性二次調整器（LQR）技術，控制代價或成本將得以納入控制器設計過程中一併考量。 並且，由於利用LQR設計PID 控制器，LQR本身所具備的強健性將有助於改善PID 控制器的性能。在應用LQR於最佳化PID控制器設計方面，文獻所見大多是針對連續系統，甚少用於離散系統。為了發展離散最佳化PID控制，首先藉由近似的概念來形成新誤差動態方程式，以利控制器之推導。此外，針對未知受控系統的系統識別，提出類神經網路（NN）與遞迴式最小平方法（RLS）模型之間的比較。本文同時亦對回授最佳化PID控制與前饋式最佳化PID控制兩種不同的架構提出討論。而當系統本身為非線性且未知時，在確知系統階數（或系統延遲）與控制輸入對系統所造成影響的前提之下，針對PID控制器的自我調變最佳化，本文提出一新穎的不等式拘限最佳化演算法，確保在迫使追蹤誤差趨近於零的同時，PID控制增益亦能藉由調整得以最小化。 對於無漣波速達控制(ripple-free deadbeat control)響應，內部模型定理乃基本之充要條件。本文應用所謂直流（低頻）增益運算子來發展一新的速達追蹤控制器（deadbeat tracking controller）。只要滿足所推導的充分條件，取樣資料系統中的漣波響應將微乎其微。 當系統狀態不可得之時，將速達狀態估測器與速達追蹤控制器結合，將可收相得益彰之效！一旦系統參數產生突然變化，對於既定常數參數的控制器而言，恐有造成系統性能惡化之虞。為此乃採用即時RLS演算法以估算新的系統參數，進而同步更新速達控制器參數，讓追蹤誤差再次收斂。 當系統存在較大的不確定時，強健控制器將無法達成較佳的性能要求。此時或可考慮使用輻射基底類神經網路（RBFNN）作為近似器，待學習效果良好之後，期與系統不確定性相消，繼之發展多變數滑動模式類神經適應控制以改善系統性能。 與類神經網路學習成效息息相關者有二：類神經網路架構與學習法則。在學習法則方面，本文針對RBFNN提出一不等式拘限最佳化演算法，期以在學習誤差持續收斂的同時，亦能最小化連結權重值。並且用誤差修正項為學習法則之其中一項，以確保連結權重值的有限性。亦即，針對RBFNN所提出之穩定學習法則，確實能改善RBFNN的學習效能。 本文所提出之控制器設計或學習法則，皆同時附有穩定性分析與模擬結果。在選定適當的李亞普諾夫之後，得以應用李亞普諾夫穩定性定理來進行系統的穩定性分析。

For a class of coupled linear, time-invariant, multi-input multi-output (MIMO) systems, a systematic method is developed according to different relative degrees of system to tune the P/PI/PID control gains. By using linear quadratic regulator (LQR) strategy, the restriction of control cost can be taken into consideration for controller designs. Furthermore, the robustness of LQR provides improvement on performance of PID control. There are few literatures on the discrete-time optimal PID control. A new error dynamic equation is established via approximation concept to construct the discrete-time optimal PID control. When the controlled plant is unknown, the comparison of the neural network (NN) and recursive least squares (RLS) model is presented for the off-line system identification. The output-sensorless optimal PID control is also discussed. When the nonlinear controlled plant is unknown except the system order (or system delay) and the sign of transmitting control input, a novel self-tuning method of optimal PID control laws is proposed based on an inequality constraint optimization mechanism to ensure the minimization of PID gains as coercing the tracking error to zero. The internal model principle is the sufficient and necessary condition to obtain the ripple-free deadbeat control response. In this dissertation, a new deadbeat tracking controller is developed by applying the so-called gain operator. Under some derived sufficient conditions, the ripple response in the sampled-data systems will be very inconspicuous. To handle the systems with unmeasured states, the deadbeat observer will be integrated with the deadbeat tracking controller. Once the system has variations on system parameters, the performance will be destroyed due to constant control gains. Therefore, the on-line recursive least squares (RLS) algorithm is adopted to estimate the new system parameters for updating the deadbeat control parameters. When the system uncertainties are large, the robust control may fail to maintain a good performance. The radial basis function neural network (RBFNN) can be employed as an approximator to compensate the system uncertainties after effective learning. Then a multivariable sliding-mode neuro-adaptive control is developed for improvement on tracking performance. Two aspects affect the approximation capability of neural networks: structure and updating law. An inequality constraint optimization mechanism, minimizing the connection weights subject to the stable reaching condition, is established to adjust the connection weights of RBFNN. Moreover, the e-modification term is utilized as another part of the stable updating law to guarantee the boundedness of connection weights. The proposed stable updating law indeed improves the learning capability of RBFNN. All the control laws and updating laws in this dissertation were justified with stability analysis and simulations. After choosing the corresponding Lyapunov function, the system stability can be guaranteed by using Lyapunov stability theory if the derived sufficient conditions are satisfied.