Enhanced Single-Loop Control Strategies Chapter 16 1. Cascade control 2. Time-delay compensation 3. Inferential control 4. Selective and override control 5. Nonlinear control 6. Adaptive control 1
Chapter 16 Example: Cascade Control 2
Chapter 16 3
Chapter 16 4
Cascade Control Chapter 16 Distinguishing features: 1. Two FB controllers but only a single control valve (or other final control element). 2. Output signal of the "master" controller is the set-point for slave" controller. 3. Two FB control loops are "nested" with the "slave" (or "secondary") control loop inside the "master" (or "primary") control loop. Terminology: slave vs. master secondary vs. primary inner vs. outer 5
Chapter 16 6
Y G 1 P1Gd2 = (16 5) D 1+ G G G G + G G G G G G 2 c2 v p2 m2 c1 c2 v p2 p1 m1 Chapter 16 Y Y 1 2 D D Y Y Y Y% 1 2 m1 m2 = hot oil temperature = fuel gas pressure = cold oil temperature (or cold oil flow rate) = supply pressure of gas fuel = measured value of hot oil temperature = measured value of fuel gas temperature = set point for sp1 1 = set point for Y Y sp2 2 7
Chapter 16 Example 16.1 Consider the block diagram in Fig. 16.4 with the following transfer functions: 5 4 Gv = Gp1= Gp2= 1 s+ 1 ( 4s+ 1)( 2s+ 1) 1 Gd2= 1 Gm1= 0.05 Gm2= 0.2 Gd1= 3s + 1 8
Chapter 16 9
Example 16.2 Compare the set-point responses for a second-order process with a time delay (min) and without the delay. The transfer function is G p ( s) = e θ s ( 5s+ 1)( 3s+ 1) ( 16 18) Chapter 16 Assume Gm= Gv= 1 and time constants in minutes. Use the following PI controllers. For θ = 0, K c = 3.02andτ1 = 6.5min, while for θ = 2 min the controller gain must be reduced to meet stability requirements K = 1.23, τ = 7.0min. ( c ) 1 10
Time Delay Compensation Chapter 16 ( ) ( ) E' = E Y% = Y Y% Y Y% 1 sp 1 2 16 19 If the process model is perfect and the disturbance is zero, then Y % 2 = Y and sp ( ) E' = Y Y % 1 16 20 For this ideal case the controller responds to the error signal that would occur if not time were present. Assuming there is no model error ( G% = G), the inner loop has the effective transfer function P G G' = = c E 1 + GG* 1 e θ c ( s ) ( 16 21) 11
Chapter 16 For no model error: G=G % G c Gc = 1+ GG 1 c θ ( e ) * s * θ s θ = G * e - s Y GGe c GG c = = Y θ 1+ GGe 1+ GG * s * sp c c By contrast, for conventional feedback control Y Y sp θ s GGe c * = θ s 1 + GGe * c ( 16 23) 12
Chapter 16 13
Chapter 16 14
Inferential Control Problem: Controlled variable cannot be measured or has large sampling period. Chapter 16 Possible solutions: 1. Control a related variable (e.g., temperature instead of composition). 2. Inferential control: Control is based on an estimate of the controlled variable. The estimate is based on available measurements. Examples: empirical relation, Kalman filter Modern term: soft sensor 15
Chapter 16 Inferential Control with Fast and Slow Measured Variables 16
Selective Control Systems & Overrides For every controlled variable, it is very desirable that there be at least one manipulated variable. Chapter 16 But for some applications, N C > N M where: N C = number of controlled variables N M = number of manipulated variables Solution: Use a selective control system or an override. Selective control is also referred as Auctioneering. 17
Low selector: Chapter 16 High selector: Median selector: The output, Z, is the median of an odd number of inputs 18
Chapter 16 Example: High Selector Control System multiple measurements one controller one final control element 19
Chapter 16 2 measurements, 2 controllers, 1 final control element 20
Chapter 16 Overrides An override is a special case of a selective control system One of the inputs is a numerical value, a limit. Used when it is desirable to limit the value of a signal (e.g., a controller output). Softer than ESD or SIS Example: - anti-reset wind-up - lower and upper heat input rate for distillation column for ensuring liquid inventory or preventing flooding of the column Split-range control 21
Chapter 16 22
Nonlinear Control Strategies Chapter 16 Most physical processes are nonlinear to some degree. Some are very nonlinear. Examples: ph, high purity distillation columns, chemical reactions with large heats of reaction. However, linear control strategies (e.g., PID) can be effective if: 1. The nonlinearities are rather mild. or, 2. A highly nonlinear process usually operates over a narrow range of conditions. For very nonlinear strategies, a nonlinear control strategy can provide significantly better control. Two general classes of nonlinear control: 1. Enhancements of conventional, linear, feedback control 2. Model-based control strategies Reference: Henson & Seborg (Ed.), 1997 book. 23
Enhancements of Conventional Feedback Control Chapter 16 We will consider three enhancements of conventional feedback control: 1. Nonlinear modifications of PID control 2. Nonlinear transformations of input or output variables 3. Controller parameter scheduling such as gain scheduling. Nonlinear Modifications of PID Control: One Example: nonlinear controller gain K = K (1 + a et ( ) ) (16-26) c c0 K c0 and a are constants, and e(t) is the error signal (e = y sp -y). Also called, error squared controller because controller output is proportional to e(t) e(t) Example: level control in surge vessels. 24
Nonlinear Transformations of Variables Chapter 16 Objective: Make the closed-loop system as linear as possible. (Why?) Typical approach: transform an input or an output. Example: logarithmic transformation of a product composition in a high purity distillation column. (cf. McCabe-Thiele diagram) x 1 x = log 1 x * D D Dsp where x* D denotes the transformed distillate composition. Related approach: Define u or y to be combinations of several variables, based on physical considerations. Example: Continuous ph neutralization CVs: ph and liquid level, h (16-27) MVs: acid and base flow rates, q A and q B Conventional approach: single-loop controllers for ph and h. Better approach: control ph by adjusting the ratio, q A / q B, and control h by adjusting their sum. Thus, u 1 = q A / q B and u 2 = q A / q B 25
Chapter 16 Gain Scheduling Objective: Make the closed-loop system as linear as possible. Basic Idea: Adjust the controller gain based on current measurements of a scheduling variable, e.g., u, y, or some other variable. Note: Requires knowledge about how the process gain changes with this measured variable. 26
Examples of Gain Scheduling Example 1. Titration curve for a strong acid-strong base neutralization. Example 2. Once through boiler The open-loop step response are shown in Fig. 16.18 for two different feedwater flow rates. Chapter 16 Fig. 16.18 Open-loop responses. Proposed control strategy: Vary controller setting with w, the fraction of full-scale (100%) flow. K = wk, τ = τ / w, τ = τ / w, (16-30) c c I I D D Compare with the IMC controller settings for Model H in Table 12.1: θ s Ke θ τ + 1 (), 2 θ τθ Model H : Gs = Kc =, τi = τ +, τd = τs + 1 K θ 2 2τ + θ τc + 2 27
Adaptive Control A general control strategy for control problems where the process or operating conditions can change significantly and unpredictably. Chapter 16 Example: Catalyst decay, equipment fouling Many different types of adaptive control strategies have been proposed. Self-Tuning Control (STC): A very well-known strategy and probably the most widely used adaptive control strategy. Basic idea: STC is a model-based approach. As process conditions change, update the model parameters by using least squares estimation and recent u & y data. Note: For predictable or measurable changes, use gain scheduling instead of adaptive control Reason: Gain scheduling is much easier to implement and less trouble prone. 28
Chapter 16 Block Diagram for Self-Tuning Control 29
Bumpless Transfer When a control loop is turned on without bumpless transfer, the process can become unduly upset. With bumpless transfer, an internal setpoint is used for the controller and the internal setpoint is ramped at a slow rate from the initial conditions to the actual desired setpoint to order to provide a smooth startup of a control loop. 30
Comparison of True and Internal Setpoints True Setpoint Internal Setpoint Time 31
Control Performance With and Without Bumpless Transfer w/o bumpless transfer w/ bumpless transfer Time 32
Split Range Flow Control In certain applications, a single flow control loop cannot provide accurate flow metering over the full range of operation. Split range flow control uses two flow controllers (one with a small control valve and one with a large control valve) in parallel. At low flow rates, the large valve is closed and the small valve provides accurate flow control. At large flow rates, both valve are open. 33
Split Range Flow Controller FC FT FT FC 34
Coordination of Control Valves for Split Range Flow Control Signal to Control Valve (%) Smaller Control Valve Larger Control Valve Total Flow Rate 35
Example for Split Range Flow Control RSP FC FT Acid Wastewater FT NaOH Solution phc pht Effluent 36
Titration Curve for a Strong Acid-Strong Base System ph 14 12 10 8 6 4 2 0 0 0.002 0.004 0.006 0.008 0.01 Base to Acid Ratio Therefore, for accurate ph control for a wide range of flow rates for acid wastewater, a split range flow controller for the NaOH is required. 37
Other Split-Range Flow Control Examples When the controlled flow rate has a turn down ratio greater than 9 See value sizing examples in Chapter 2 38
Split Range Temperature Control Cooling Water Split-Range Temperature Controller Steam TT RSP TT TC 39
Split Range Temperature Control 100 Signal to Control Valve (%) 80 60 40 20 0 Cooling Water Steam Error from Setpoint for Jacket Temperature 40
Overview All controllers that employ integral action should have anti-reset windup applied. Bumpless transfer provides a means for smooth startup of a control loop. When accurate metering of a flow over a very wide flow rate range is called for, use split range flow control. 41
Bumpless Transfer When a control loop is turned on without bumpless transfer, the process can become unduly upset. With bumpless transfer, an internal setpoint is used for the controller and the internal setpoint is ramped at a slow rate from the initial conditions to the actual desired setpoint to order to provide a smooth startup of a control loop. 42
Comparison of True and Internal Setpoints True Setpoint Internal Setpoint Time 43
Control Performance With and Without Bumpless Transfer w/o bumpless transfer w/ bumpless transfer Time 44
Split Range Flow Control In certain applications, a single flow control loop cannot provide accurate flow metering over the full range of operation. Split range flow control uses two flow controllers (one with a small control valve and one with a large control valve) in parallel. At low flow rates, the large valve is closed and the small valve provides accurate flow control. At large flow rates, both valve are open. 45
Split Range Flow Controller FC FT FT FC 46
Coordination of Control Valves for Split Range Flow Control Signal to Control Valve (%) Smaller Control Valve Larger Control Valve Total Flow Rate 47
Example for Split Range Flow Control RSP FC FT Acid Wastewater FT NaOH Solution phc pht Effluent 48
Titration Curve for a Strong Acid-Strong Base System ph 14 12 10 8 6 4 2 0 0 0.002 0.004 0.006 0.008 0.01 Base to Acid Ratio Therefore, for accurate ph control for a wide range of flow rates for acid wastewater, a split range flow controller for the NaOH is required. 49
Other Split-Range Flow Control Examples When the controlled flow rate has a turn down ratio greater than 9 See value sizing examples in Chapter 2 50
Split Range Temperature Control Cooling Water Split-Range Temperature Controller Steam TT RSP TT TC 51
Split Range Temperature Control 100 Signal to Control Valve (%) 80 60 40 20 0 Cooling Water Steam Error from Setpoint for Jacket Temperature 52
Overview All controllers that employ integral action should have anti-reset windup applied. Bumpless transfer provides a means for smooth startup of a control loop. When accurate metering of a flow over a very wide flow rate range is called for, use split range flow control. 53